Assuming you believe that the historical figure existed, and also factoring in the Jewish family system of the time, how likely is it that perhaps the Carpenter had children. Perhaps there are offspring of Yeshua roaming the earth as we speak and we don’t even know!
Few serious academic scholars deny that the historical figure of Jesus existed. Debate over his work, ministry, and claims to divinity (in a monotheistic Judaism), and miracles are hotly disputed. But modern, recent, scholarship tends to acknowledge he existed around the time stated.
The issue of offspring or marriage is more perplexing because it would have been normal and natural for him to prepare for marriage in his mid 20s for a younger bride, probably mid teens(ish). That being said, the 4 biographies if his life, the gospel accounts, which are history, dont mention anything at all about spouse or children. One could reasonably exoect some mention of a spouse in how she helped him in his ministry etc.
A potential mitigating factor is that traditional Jewish and Roman families had an expectation that one prepare for marriage by being in a stable job and therefore a somewhat reliable income. Jesus, as a handiman and itinerant teach/preacher may not have qualified in such a way because he had no home of his own (most likely), and because he travelled a lot.
It wouldnt necessarily be something to expect to be mentioned in his biographies as other biographies of the time focus on notable achievements and family are therefore only mentioned when pertinent to the narrative or event (such as, for example, Caesar's daughter - married to Pompey, or Pilot's wife - her dream).
Also, they weren't written like biographies of today; as with most ancient biographical accounts, they are written to demonstrate a purpose or point (cinsider Augustus' Res Gestae, for example, or Suetonius' 12 Caesars).
In terms of children, it seems significantly important that no child has ever been mentioned (pitside of Dan Brown's novels), particularly as an influential figure in the fledgling movement. Typically, a close heir would take the reins of such a potentially vibrant and expanding and therefore popular and populist movement, and the fact none did, and that there was no apparent internal struggle, but it was shared amongst his dedicated followers and his brother James in Jersualem, it seems highly unlikely that he had any children.
All that to say, we dont know, but based on the evidence, it seems plausible but unlikely Jesus of Nazareth was married. Much less likely to suggest he had kiddos.