Vishnu tells Narada in the Narayaniya portion of the Shanti Parva in Mahabharata:
Assuming a form that is manifest, I dwell, at present, in the heavens. At the end of a thousand Yugas I shall once more with-draw the universe into myself. Having withdrawn all creatures, mobile and immobile into myself, I shall exist all alone with knowledge only for my companion. After the lapse of ages I shall again create the universe, with the aid of that knowledge. That which is my fourth form creates the indestructible Sesha. That Sesha is called by the name of Sankarshana. Sankarshana creates Pradyumna. From Pradyumna I take birth myself as Aniruddha. I create (myself) repeatedly. From Aniruddha springs Brahma. The latter takes birth from Aniruddha's navel. From Brahma spring all creatures mobile and immobile. Know that Creation springs in this way repeatedly at the beginning of every Kalpa.
At the end of 1000 yugas, Vishnu withdraws everything into himself including Adi Sesha as he says only after starting the creation process again, does he create Adi Sesha once more. So from the above it can be inferred that after the universe is withdrawn, Adi Sesha does not exist for a particular time period. He does mention that he exists alone with his companion, which in itself is a contradictory statement as if he exists alone, then there cannot be any companion and if there is companion, then he cannot exist alone.
But here is what Vishnu Purana says:
Janárddana, invested with the quality of darkness, assumes the awful form of Rudra, and swallows up the universe. Having thus devoured all things, and converted the world into one vast ocean, the Supreme reposes upon his mighty serpent couch amidst the deep: he awakes after a season, and again, as Brahmá, becomes the author of creation.
Vishnu Purana says after Vishnu swallows the universe, he reposes on his serpent - Adi Sesha. But as per Vishnu's own statement, Adi Sesha cannot exist once the universe is swallowed as everything from mobile to immobile is also withdrawn and Adi Sesha is only created once the creation process starts again.
The above two statements from Mahabharata and Vishnu Purana seem contradictory, how to resolve this contradiction?