Do you think Jason would ever try and adopt kids of his own? I imagine he'd be beyond happy to have a family of his own even if he would need to leave the vigilante lifestyle behind but also wouldn't really imagine something like that being possible for himself in the first place. For several reasons.

First and foremost, we all need to be on the same page that Jason is canonically really good with kids. It's also canon that Jason has some of the worst familial luck in the world.

I think, to Jason, starting a family would be one of his pipe dreams. He knows intimately not every person should be a parent. That it's a parent's job to put their kid first and not every adult is capable of doing that. Jason predominately had to raise himself and had very little guidance as a young child from the adults around him. He's been on the receiving end of taking care of the adults who should've been taking care of him and has had their trauma/issues projected onto him his entire life. Jason has no idea where to start with raising a child. The only stepping stones he has are "Don't do what was done to you as a child" and "What did I need as a child?" Which can be helpful tools, but aren't stable foundations to raise a child on. To this day, Jason still doesn't know how he should actually be treated as a living human being. While he can usually reciprocate needs to others, he's constantly overshadowed by this weight that he's doing everything wrong.

Jason is pretty self-aware and he knows how damaging it is to be on the receiving end of a parent who's not capable of raising a kid. Whether he faults those adults or not, he would blame himself because he would be actively choosing to have a kid. Jason knows he's fucked up and he wouldn't want to fuck a kid up like how he was. Especially because Bruce did do that with a multiple of his: "I didn't want them to turn into me." Even further, Jason doesn't even pursue most (romantic) relationships because he's well aware of his many issues and enemies and how that can lead to many problems. In what world would he feel comfortable putting a child in that position if he fears projecting onto and/or damaging a fellow adult? I think he'd even view it as being selfish. How he's only adopting a child because "he wants one," "wants to help them," "etc." because again that didn't turn out well for Jason. The man knows he'd have to achieve a spectacular amount of healing before he'd be capable of raising a child and Jason doesn't fully know how or if he can heal from the life he's led. Besides that, Jason would constantly be worried about his old life coming back to haunt his new one.

The only way I could see him adopting kids would be if he left the vigilante business (which neither he nor I see happening) and probably somewhat cutting ties with the bats. Whether because of rocky relationships or because he knows being in contact with them would only allow trouble to lead back to him and the new life he's made. Like if Jason was hypothetically a parent, I don't think he'd trust himself to leave his kids around Bruce. If something were to happen to his kids (like killed by an enemy hypothetically), he knows damn well Bruce won't do anything about it except try to stop Jason from putting an end to whoever hurt his loved ones. He would Especially not let them be his sidekick. I know Scarlett and Duela, two girls people like putting as "his" (which ignores the fact that he and Duela used to be the same age. Before that, her older than him), were already loosely ~in the bizz~ so to speak, but he actively encouraged both girls to leave and be something more. Tyler, on the other hand, I hate how fandom always forgets his mom is right there and still around? Yes, she was in the hospital, but people forget that she got better and is getting help. Very dismissive and, to me, comes off as incredibly uncouth.

This isn't to say Jason doesn't know anything about kids and child care. I think Jason knows logically that X is abusive and can do Y to a child's development. But I think his own fears, insecurities, and rightfully placed concerns+considerations would get in the way of ever truly considering kids of his own. In fact, I think that's one of the things that could make Jason a really good parent: He knows that not everyone should be one.

TL;DR No, I don't think Jason would ever adopt/have kids in general because he fears doing to them what was done to him. I.E. Pushing and projecting trauma onto a kid because he knows he doesn't have the skills to be a long-time caretaker to a child. Let that man heal. Slapping him with a kid won't actually do that. You can argue he could "break the cycle of abuse," but I truly think Jason is too terrified to even attempt that because he knows that kids are actually their own person too and deserve to be treated as such. He would never adopt "Just because he's always wanted a kid/start a family of his own."

Really, most takes I see with giving Jason kids are because people either want to squeeze him out of vigilantism or so he can "be more like Bruce" with the adoption tendencies. Neither falls in line with canon Jason while also confusing long-term care = "being good with kids" which are not the same things.