Srimathe Ramanujaya Namah! Sri Sriranga Narayana Jeeyar Swamigale Saranam!
In Bhagavatham Canto 5, Chapter 4, Verse 1, Suka Brahmam details the symptoms of the Lord who incarnated as Lord Rshba Deva
atha ha tam utpattyaivābhivyajyamāna-bhagaval-lakṣaṇaṁ sāmyopaśama-vairāgyaiśvarya-mahā-vibhūtibhir anudinam edhamānānubhāvaṁ prakṛtayaḥ prajā brāhmaṇā devatāś cāvani-tala-samavanāyātitarāṁ jagṛdhuḥ.
Krishna or Narayana is the Supreme Lord Himself in His complete form as stated in Bhagavatham (1.3.28)
ete cāṁśa-kalāḥ puṁsaḥ kṛṣṇas tu bhagavān svayam indrāri-vyākulaṁ lokaṁ mṛḍayanti yuge yuge
Every Avatararam (even the channa avatars like Chaitanya Mahaprabhu Ref: 11.5.32) and Alwars / Acharyas (11.5.38-40) are mentioned in Srimad Bhagavatham. So anyone claiming them as God has to back their claim through bonafide scriptures.
Badrinarayana Ramanuja Dasan