I want to know more about Yami. It is believed that there was a twin sister of
The story is described in chapter 77 of the Markandeya Purana:
The daughter of Vishwakarman [the divine architect] was the wife of the sun, by name Sajna who begat on her a son, by name Manu, who, illustrious as he was, was equally a master of various branches of learning. He was the son of Vivaswat and was therefore called Vaivaswata. As soon as she was espied by the sun Sajna used to close her eyes and therefore he, in anger, addressed to her cruel words: "Since, O stupid one, you close yours eyes as soon as I cast my looks on you therefore will you give birth to Yama, the destroyer of creatures." Thereupon the goddess, stricken with fear, assumed trembling looks, at which the sun again said to her. "Since beholding me, you have assumed trembling looks you will give birth, as your daughter, to the fickle river." Thus by the imprecation of her husband she gave birth to Yama and the great river celebrated under the name of Yamuna. Henceforth she, with great difficulty, began to suffer the effulgence of the sun.
By the way, in case you're interested that isn't how the story ends: after that Sanjana leaves Surya, because she cannot take his brightness and she's replaced with her shadow Chaya, who pretends to be Sanjana. You can find out about the rest of the story in my answer here.
Yami is none other than Devi Yamuna.
4-5. O sage, the sun begot three offsprings of her: the patriarch Manu Śrāddhadeva, Yama and Yamunā born as twins.
40-42. The lord is performing penance even today on the top of Meru. Their younger sister, the famous Yamī, became the most excellent river Yamunā, the sanctifier of all the worlds. He is called Sāvarṇi Manu in the world. He who listens to or retains in memory this origin of the gods attains great fame. Should he suffer from any adversity he will be rid of it.
S.B. 6:6:40. Of Vivasvân gave the fortunate Samjñâ birth to the Manu called S'râddhadeva as well as to the demigod Yamarâja and his sister Yamî [the river Yamunâ]. She also, having become a mare, gave birth on this earth to the As'vinî-kumâras.
Vishnu Purana 3:2. Sañjñā, the daughter of Viśvakarman, was the wife of the sun, and bore him three children, the Manu (Vaivaswata), Yama, and the goddess Yamī (or the Yamunā river).
Brahmanda Purana 3:59. 22-24. The daughter of Tvaṣṭṛ who became well-known, as Saṃjñā and the wife of Savitṛ (the Sun) gave birth to Manu, the eldest son of great fortune and exalted dignity, of Vivasvān. (the sun). The she gave birth to the twins viz. Yama and Yamunā (See vv 31-32 where Yama and Yamī are the names mentioned). She assumed the form of a mare and went to the Kurus.
Harivaṃśa Purāṇa also describes Yama and Yamī (Yamunā) to be twins, besides other scriptures.
Chapter 9, Harivamsa Parva, Harivaṃśa Purāṇa
त्रीण्यपत्यानि कौरव्य संज्ञायां तपतां वरः ।
आदित्यो जनयामास कन्यां द्वौ च प्रजापती ॥ ७ ॥
- O foremost of Kauravas, that best of luminous bodies, Aditya begat on Sajna three children, one daughter and two sons who became patriarchs.
मनुर्वैवस्वतः पूर्वं श्राद्धदेवः प्रजापतिः ।
यमश्च यमुना चैव यमजौ सम्बभूवतुः ॥ ८ ॥
- First was born Manu Vaivasvata and then the patriarch Sraddhadeva, then Yama and Yamuna were born as twins.
English Translation by M.N. Dutt
The story is also narrated in the Chapter 59, Upodghāta-pāda of the Brahmāṇḍapurāṇa, as I discuss in this answer.