Yes, one Krishna took birth simultaneously in 2 forms in the wombs of Yasoda and Devaki. However, they are same not like the two Krishna theory suggested by modern interpretations. Krishna in Vrindavan is predominated by sweetness and in Dvaraka or Mathura, there is predomination of aisvarya(opulence).
Bhagavata 10.3.8
niśīthe tama-udbhūte jāyamāne janārdane |
devakyāṁ deva-rūpiṇyāṁ viṣṇuḥ sarva-guhā-śayaḥ |
āvirāsīd yathā prācyāṁ diśīndur iva puṣkalaḥ ||
niśīthe—in the middle of the night; tamaḥ-udbhūte—in which there was an
increase of darkness (or intensely pervaded by darkness); jāyamāne janārdane—
when Janārdana was taking birth; devakyām—to Devakī (‘having taken Devakī
as the support’, āśraya-saptamī); deva-rūpiṇyām—whose form is like the Lord’s;
viṣṇuḥ—Viṣṇu; sarva-guhā-śayaḥ—who reposes in all secret places (or who is
the abode (āśaya) of all secret places); āvirāsīt—made His appearance; yathā
—suitably; prācyām—which is the east; diśi—in the direction; induḥ iva—like a
moon; puṣkalaḥ—full.
Syntactical connection of the verse is as follows:
tama-udbhūte niśīthe deva-rūpiṇyāṁ devakyāṁ (vraja-nātha-patnyāṁ)
janārdane jāyamāne, prācyāṁ diśi puṣkalaḥ induḥ iva (āvirbhavati), viṣṇuḥ
sarva-guhā-śayaḥ (deva-rūpiṇyāṁ devakyāṁ śauri-patnyāṁ) yathā (yathā =
yathāvat) āvirāsīt.
This is one verse of six lines.
“When Hari was appearing (janārdane jāyamāne
= harau prādurbhavati sati) to Devakī, Nanda’s wife (devakyām = vraja-nāthapatnyām),
when the middle of the night was intensely pervaded by darkness
(niśīthe tama-udbhūte = ardha-rātre tamasā utkarṣeṇa bhūte vyāpte sati)—since
a series of clouds came forth out of nowhere—Viṣṇu, who is that same
Janārdana, suitably appeared, as a form that was already perfect before (yathā =
yathāvat = pūrva-siddhena eva rūpeṇa), to Devakī, Vasudeva’s wife (devakyām
= śauri-patnyām).”
Owing to the locative absolute, a simultaneous birth in two places is made to
be understood.
This is also known from Sri Hari-vamsa:
garbha-kāle tv asampūrṇe aṣṭame māsi te striyau |
devakī ca yaśodā ca suṣuvāte samaṁ tadā || “During the eighth month, when the pregnancy
had not reached maturity, those two ladies, Devaki and Yasoda, gave
birth at the same time.” (Harivamsa
2.4.11)
However, Bhagavata states:
SB 10.3.47: Afterward, Śauri was impelled by the Lord. When he,
taking his son, intended to go out of the maternity room, birthless
Yogamāyā took birth by Nanda’s wife
In the sentence of Hari-vaṁśa, the sense is that they gave birth at exactly the
same time (samam = saha = sama-kālam eva). Since there is a discrepancy
between the two scriptural statements, in Hari-vaṁśa and in Bhāgavatam,
because in the former one meaning is understood but in the latter it is shown that
Yaśodā gave birth after Devakī did, it is ascertained as follows: Yaśodā gave
birth to Kṛṣṇa exactly when Devakī gave birth to Kṛṣṇa, and at a later time
Yaśodā also gave birth to Yogamāyā. She had two childbirths by a difference in
time. For that reason it will be said: adṛśyatānujā viṣṇoḥ sāyudhāṣṭa-mahābhujā,
“Viṣṇu’s younger sister was seen: She had eight great arms with weapons”
(Bhāgavatam 10.4.9). This statement has no meaning if both didn't take birth from Yashoda's womb.
In this way Yasoda had a pair of offsprings, a boy and a
girl. It is understood that the pair was perceived neither by Vasudeva nor by
Yasoda.
Here(SB 10.3.8), Yasoda too is expressed with the word devakyam.
For example there is a
statement in Adi Purana:
dve nāmnī nanda-bhāryāyā yaśodā devakīti ca |
ataḥ sakhyam abhūt tasyā devakyā śauri-jāyayā ||
“Nanda’ wife had two names: Yasoda and Devaki, therefore she developed
friendship with Devaki, Vasudeva’s wife.”
By the logical reasoning of a lamp located in the threshold of a door (dehalīpradīpa-
nyāya) (also called kākākṣi-nyāya), the syntactical connection of
devakyām occurs in both places, due to the appropriateness of the reading
between jāyamāne janārdane and viṣṇuḥ. (See the syntactical connection of the
verse.)
In the current verse, this is perceived: Just as Vasudeva is an avesa of Hari, in
accordance with avivesamsa-bhagena, “The Lord,with full identity,
entered Vasudeva’s mind” (Bhagavatam 10.2.16), Nanda too is an avesa of the
Lord, on account of inferential characteristics in the following texts:
(A) nandas tv atmaja utpanne jatahladah, “When a son was born, Nanda
became overjoyed ” (10.5.1),
(B) nandah sva-putram adaya, “Nanda took his son” (10.6.43), and
(C) pasupangajaya, “[Brahma said: “I offer obeisances] to the son of a
cowherd”” (10.14.1). As Vasudeva channelled the Lord in Devaki, so
Nanda channelled the Lord in Yasoda, as in the case of a guru and a
disciple.
However, due to the Lord’s order, Durga entered Yasoda’s womb much like
Sankarsana entered Rohini’s womb, on account of the two verses that begin
from: devakya jathare garbham, “[Sri Krsna said to Yogamaya:] My dhama
known as Sesa is in Devaki’s uterus. Pull Him out of there and place Him in
Rohini’s womb. O splendid one, afterward, with my full identity, I will
become Devaki’s son and you will manifest in Yasoda, Nanda’s wife”
(Bhagavatam 10.2.8-9).
In Vrindavan also, The cowherds who were King Nanda’s doorkeepers fell asleep
because of Yoga-nidrā, a superior aṁśa, and all the doors opened by themselves.
Yaśodā fell asleep only because of her. Vasudeva did not see her son. He placed
his own son there, took her daughter and went back. It is understood that the two
newborn sons became one, just like two broken clouds merge
Hari is the legitimate son of Yaśodā like He is the legitimate son of Devakī.
For instance: yaśodā nanda-patnī ca, “Yaśodā, Nanda’s wife, [only understood
that there was a birth. Being fatigued, and her memory hampered by sleep, she
did not know the child’s gender]” (Bhāgavatam 10.3.53).
In below verses Krishna is addressed many times as own son of Yashoda and Nanda by Shukadeva, Brahma etc.: And all need to be taken in direct sense.
nandagopa-
gṛhe putro yaśodā-garbha-sambhavaḥ, “A son was born from Yaśodā’s
womb, in the house of Nanda the cowherd” in Ādi Purāṇa, and similarly: nandas
tv ātmaja utpanne jātāhlādaḥ, “When a son was born, Nanda became overjoyed”
(Bhāgavatam 10.5.1), and nayam sukhapo
bhagavan dehinam gopika-sutah (Bhagavatam 10.9.21) The Supreme
Personality of Godhead, Krsna, the son of mother Yasoda, is accessible
to devotees engaged in spontaneous loving service, but not to the
materialist. and nandah sva-putram adaya pretyagatam
udara-dhih(10.6.43) Simple and liberal Nanda took his son, who had
returned from death. pasupangajaya, “[Brahma said: “I offer obeisances] to the son of a
cowherd”” (10.14.1)
However, when Devaki spoke to Kamsa, she was trying to hide the fact of her son's birth by saying the eighth child was a daughter and thus SB 10.4.7 can't be taken literally.
Why did Sukadeva not state the birth of Krsna from Yasoda directly?
One should accept it as Lord's intention: Even the
sage (Sukadeva), under the influence of the Lord, spoke of Him in a hidden way.
"I will appear in the house of both Nanda and Vasudeva. I will however remain only in Nanda's house with one form. If I have two forms, Kamsa will know that I hve taken birth and will persecute both sets of parents. You(Sukadeva) should recite my story so that the secret is not revealed". This is the intention of the Lord. Accepting the Lord's desire, the author wrote the book accordingly.
Vallabhacharya, of Rudra Sampradaya or Pushtimarg commenting on Bhagavatam 10.2.16 says that Krishna took birth as son of Yashoda:
“The Lord entered Ānakadundubhi’s heart along with the category of aṁśas
(aṁśa-bhāgena = aṁśānāṁ vibhāgena).” However, some say: “He entered with
a part, in the form of hair, which is an aṁśa in the form of Nārāyaṇa (aṁśabhāgena
= aṁśena nārāyaṇa-rūpeṇa bhāgena keśa-rūpeṇa saha), but
Puruṣottama took birth with Yogamāyā, only in Nanda’s home,” otherwise there
is a contradiction with: nandas tv ātmaja utpanne jātāhlādaḥ, “When his son
was born, Nanda became overjoyed” (Bhāgavatam 10.5.1).
References are: Laghu Bhagavatamrita of Rupa Goswami, Vaishnava Nandini of Baladeva Vidyabhusana, Subhodini of Vallabhacharya, Symphony of commentaries on 10th Canto.
