His biological father has never been shown and it is never explained what happened to him.
From Season 6 onward, Sanjay stopped appearing almost completely. His last speaking role was in Old Man and the C-. After that he only had cameo appearances.
He may be a relative of Ravi in the live-action movie due to the fact that Ravi appears to be of Indian descent and like Timmy he wears a pink baseball cap. Given Sanjay's admiration of Timmy, he may have given Ravi the pink cap to honor his friendship with Timmy. However, nothing shown on the screen indicates this and Sanjay himself doesn't appear in the live-action movie.
Along with Elmer, Sanjay is considered by Timmy to be his backup friend as stated in Escape From Unwish Island.
Sanjay was possibly inspired in Milhouse Van Houten and Apu Nahasapeemapetilon from The Simpsons, which Butch Hartman himself is a fan of that show. The only differences are that Sanjay has brown skin, black hair and black glasses, while Milhouse has yellow skin, a big nose, blue hair and red glasses.
An adult character from The Simpsons is also called Sanjay, who in the series, is the brother of Apu Nahasapeemapetilon.
Sanjay shares the same name with a co-star of another Nickelodeon animated series, Sanjay and Craig.
In Merry Wishmas, Tootie wishes for a pony named Timmy because she has a huge crush on him. Similarly, Sanjay wishes for a bunch of elephants all named Timmy, implying he may also have a crush on Timmy. Additionally, in Stupid Cupid, Sanjay dates a genderbent Timmy named Kimmy.
it is unknown that Sanjay's last name is not heard or even seen since it has never been revealed in the whole series or even such that no one has ever said or seen at all
Quotes
[About the Cream Puffs] "I like their knee socks!"
"This cupcake, it sparkles like the morning dew on the back of the hooded cobra!"
"Hi Timmy, it's me, Sanjay!"
[While Timmy shows his muscles at the beach]"Oh my gosh! His newly muscles self moves with the power and grace of bengal tiger"
[After seen the Silvestre Clazone movie]"And his oil chest. What?"