Can anybody refer to any Hindu text (along with the verse number, full verse and meaning) where this phrase - "oṁ namo bhagavate vāsudevāya" appears?
By the way, it is not the first verse of Srimad Bhagavatam as many people think based on the ISKCON translation. For details see Is "Krishna" mentioned in the first verse of Srimadbhagavad?
It may have appeared in other texts as well, but it's definitely in the Bhagavata Purana; the very first line, in fact!
ॐ नमो भगवते वासुदेवाय॥
जन्माद्यस्य यतोऽन्वयादितरतश्चार्थेष्वभिज्ञः स्वराट् तेने ब्रह्म हृदा य आदिकवये मुह्यन्ति यत्सूरयः।
तेजोवारिमृदां यथा विनिमयो यत्र त्रिसर्गोऽमृषा धाम्ना स्वेन सदा निरस्तकुहकं सत्यं परं धीमहि॥१॥
Om̐ namo bhagavate vāsudevāya||
Janmādyasya yato'nvayāditarataścārtheṣvabhijñaḥ svarāṭ tene brahma hṛdā ya ādikavaye muhyanti yatsūrayaḥ|
Tejovārimṛdāṁ yathā vinimayo yatra trisargo'mṛṣā dhāmnā svena sadā nirastakuhakaṁ satyaṁ paraṁ dhīmahi ||1||
So I guess the verse number would be 1.1.1.
And the translation is also in the link above, though there's a more extended analysis here.
The sloka itself is known as the Dvadasaksari mantra, as @অনু notes in a comment, and Wisdomlib shows that the mantra itself is referenced in the Parama Samhita, as well as some other texts, including the Garuda Purana.
