INFO: Can you agree to an informal arrangement where the stepson visits you along with his siblings. You don't need a formal judgement or child support for that. This way you aren't on the hook for support or anything like that. This way nothing changes for the boy in that he, for all intents and purposes, hasn't had any perceptible change in his relationship with you other that you don't live with his mum anymore just like his half siblings (which is what she and the boy want). If she really only cares about him having you as a father figure and not support, this shouldn't be an issue.

That is, unless you don't want to hold that role, of course. Then, I suppose, stick to your guns. But if you love this boy at all, please consider allowing him in your life. You don't owe him that, but it would make you a kind person.