his father is Mr. Summer

Beyond me, too.

FAIR WARNING. THIS IS A SPOILER.
I don't think we are told. I read the novel 40 years ago (all three volumes of it) and I don't remember that we are told the name of Tom's father - it certainly wasn't the faithful barber, Partridge who got the blame (and the sack) initially. But his natural mother is Squire Allworthy's sister, Brigitte who later married a Mr Blifill as I recall. She it was who placed (or arranged for) the infant Tom to be placed the Squire's bed. The scheme is only revealed when lawyer Dowding acknowledges that he gave the revealing document to the young Mr Blifill following his mother's funeral - a consequence of an accident in a carriage. Young Blifill is finally challenged as to the whereabouts of the document by Squire Allworthy in London, shortly before Tom Jones is to be hanged at Tyburn for severely injuring another character in a duel.
But best of all, watch the 1963 movie on dvd and admire the young and beautiful Sophie who is played by Susannah York to perfection! Why people do not love this charming 18th century tale is beyond me.