I came to know of some sons of Lord Vishnu but they were not with Goddess Lakshmi but with some other women. According to Chapter 22, verse 47 of ShataRudraSamhita in Shiva Purana, Lord Vishnu had begot sons with some damsels (apsaras) born after the Samudra Manthan. These sons created a lot of havoc on earth and in heaven causing misery to all, therefore on request of Gods, Lord Shiva later killed them all by taking an incarnation of a bull. Here is the extract from the ShataRudraSamhita:

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  [1]: http://i.stack.imgur.com/uDa8A.jpg