Lord Vishnu,without Lakshmi, desirous of Male child worshiped Lord Shiva at Tiruvarur.
He was blessed with a Male child, Kaama or Manmatha, the God of Love/Lust.
Angered at being omitted Lakshmi cursed Vishnu that His son would be burnt by Shiva.
Upon realization of the curse, an aggrieved Vishnu created a composite image featuring Shiva, Uma and Skanda (Somaskanda – symbolic of fertility) and offered worship to it.
Parvati alleviated the curse placed on him stating that despite being burnt to death, Kaama would live on to create the forces of attraction between the male and the female that would ensure the continuation of the human race.
There is no other children of Vishnu or Vishnu and Lakshmi, from the Purarnic references.