As one can understand the different incarnations for different millenniums by referring to Vedic literature, one can similarly understand who actually is the incarnation of Godhead in this age of Kali. In this way, the Lord especially stressed reference to authoritative scriptures. In other words, one should not whimsically accept a person as an incarnation but should try to understand the characteristics of an incarnation by referring to scriptures. An incarnation of the Supreme Lord never declares Himself to be an incarnation, but His followers must ascertain who is an incarnation and who is a pretender by referring to authoritative scriptures.
Any intelligent person can understand the characteristics of an avatara by understanding two features – the principal feature, called personality, and the marginal features. In the scriptures, there are descriptions of the characteristics of the body and the activities of an incarnation, and the description of the body is the principal feature by which an incarnation can be identified. The activities of the incarnation are the marginal features. This is confirmed at the beginning of Srimad-Bhagavatam (1.1.1) where the features of an avatara are nicely described. In that verse, the two terms param and Satyam are used, and Lord Caitanya indicates that these words reveal Kṛṣṇa’s principal feature. The other marginal features indicate that He taught Vedic knowledge to Brahma and incarnated as the purusa-avatara to create the cosmic manifestation. These are occasional features manifest for some special purpose. One should be able to understand and distinguish the principal and marginal features of an avatara. No one can declare himself an incarnation without referring to these features. An intelligent man will not accept anyone as an avatara without studying the principal and marginal features.
Source: A.C. Bhaktivedanta Swami Prabhupada (2012 edition), “Teachings of Lord Caitanya, The Golden Avatara”, Page 102