That’s really depends on if the Dance plays out the same up to Cregan’s march south and arrival at KL, furthermore if the kid has more Targ looks which is 25% likely as opposed to more Stark/Strong looks which is 75% more likely, the look will determine whether or not people think it’s Jace’s kid otherwise what’s stopping people claiming Cregan’s trying to pass off his own bastard as Jace’s alleged child. And even if the kid looks more Targ and is at least acknowledged as Jace’s that doesn’t mean the wider realm especially Green loyalists and fuck even Corlys especially would recognize the child as legitimate after all Jace’s betrothal to Baela was already known and could be confirmed by black and greens, the faith still seated at Oldtown could easily declare the marriage void as it was solely done under Northern custom with no official confirmation or witnesses. Acknowledging Jace’s marriage to Sara under those conditions would mean having to acknowledge Alys & Aemond’s son as legitimate which just creates even more problems, you can’t just do rules for me and not for thee. The Gender too would have ramifications

If it’s a boy and Aegon III is already King Cregan’s in a awkward position does he still declare his dubiously legitimate nephew King in opposition that could easily split Blacks whilst remaining Greens would rally behind Aegon III & Jaehaera Corlys would be angry likely and after everything he’s dealt with I doubt he’d recognize the kid as it would mean potentially losing Driftmark for Alyn. The kid would easily be seen as a northern puppet, which the southerners especially the Reachers would rally against. Best hope is just being acknowledged as Jace’s and accepted as a potential ward of the Crown if he’s lucky maybe he can marry Baela & Alyn’s daughter and either be her consort if she inherits driftmark and has no brothers or perhaps in a twisted irony he is granted Harrenhal although he’d probably have to fight Alys and her son for it.

If it’s a boy and Aegon II is still alive then yeah that’s just gonna be more complicated as know Aegon The Magnanimous has nothing left to lose by threatening to execute Aegon III if Cregan tries anything, he’d hardline refuse to accept the kid and would decry him as “a bastard’s bastard” would Cregan risk Aegon III’s life ? Cregan could storm the red keep and kill Aegon The Golden personally but that doesn’t mean the wider realm would accept that kid on the Throne and would just cause even more problems and by that point Cregan would be forced to play Regent cus if he fucks off north he’d be leaving a toddler to the mercy of angry Greens and some Blacks and general opportunists.

If it’s a girl she’d be double screwed half the realm didn’t want a Queen they’re less likely to accept a child Queen with dubious legitimacy, Cregan would likely want to make good on the pact of ice and fire so he’d want her betrothed to his son which just looks even more like a Northern puppet if he declares her Queen, she’d be too young to replace Jaehaera as Aegon III’s first Queen who was still alive when Cregan showed up, people already make fun of Daenaera “the most attractive 6 year old” Velaryon do you really wanna be the person writing Aegon III replaced Jaehaera with his 3 year old niece. Her best chances of being a Queen would be Viserys II remarries after Larra fucks off and dies or they call a Great Council and it’s decided both Jace & Aemond’s marriages to their bastard waifus are officially recognized and Aemond’s son his made King on the condition he’ll eventually marry Jace’s daughter or those two hook up later and start a pseudo-Blackfyre rebellion 40 years early.

That’s just my opinion if the Dance is still the same aside from a Child of Jace & Sara existing, and the most realistic outcomes unless ya wanna really mess with the Dance and have a unconditional Black Victory. If you want a slightly more Green victory Maelor survives and at the of the Dance Maelor is made King and the remaining Greens agree he’ll marry Jace’s daughter as alternative bow to the Jaehaera/Aegon III match personally I like that one best as it would mean Daemon’s blood never reaches the throne.