This is a reference to Kṛṣṇa (Krishna). Mahābhārata (Mahabharata) has defined the word adhokṣaja (adhokshaja) as such— adhokṣaja is one the lower part of whose body never undergoes any decay, that is, one who never descends or goes downwards—adho na kṣīyate jātu yasmāttasmādadhokṣajaḥ.

According to the annotator Nīlakaṇṭha (Nilakantha), the word has been compounded in such a manner that the sense of the latter part of the compound has been lost. Ideally, the meaning of this word should have been—one, the lower part of whose body never weakens, and hence, he is truly always upstanding, untouched by the material world, his movement is always upwards.

Once again, in a glossary Śāntiparva (Shantiparva) it is said that both the earth and sky face all directions, meaning, the doors of both are freely open on all sides. The earth is the the lower part or base of the form, and akṣi (akshi)—coming from akṣa (aksha) meaning sky—the upper part. One who bears both effortlessly is known as Adhokṣaja—

pṛthivīnabhasī cobhe viśrute visvatomukhe.
tayo sandhāraṇārthaṃ hi māmadhokṣajamañjasā.

Nīlakaṇṭha has further defined the word. According to Pānini’s (Panini’s) formula/principle of ‘aniditām‘ (aniditam), if the verbal root ‘sañj‘ (sanj) is added as a ka-inflection after the word ‘adhok‘, ‘na’-kāra (kara, or the post-consonantal symbol) is removed from the verbal root sañj. Following this, according to the principle of ‘suṣāmāditvāt‘ (sushamaditwat), the ‘sa’-kāra of the sañj verbal root changes to ṣa-kāra (sha-kara). Therefore, the result is,

adhok—saj–ka (a)

adhok—sañj—ka = adhok—saj + ka(a) = adhok—ṣaja (shaja) = adhokṣaja

In Anuśāsanaparva (Anushasanaparva) of Mahābhārata, where the one thousand names of God Viṣṇu (Vishnu) are mentioned in the Sahasranāmastotra (Sahrasranamastotra), Kṛṣṇa and Viṣṇu are seen as one, and hence Viṣṇu has also been referred to as Adhokṣaja.