Entry denial plus his overtstays will most definitely negatively influence any long visa application. Even agencies (well, legitimate ones with good reputations) have limits to what kind of problem kids they're willing to deal with regardless of how much they can charge the suckers. But yea, it isn;t a ban per se.....I'd give it a 40% chance of success.
You're beyond even agency help. Zero chance of getting in (even if you manage to do an e-visa) for about 1-2 years, and after that you better have a real long stay visa.
My point is that Thailand is way more advanced than the West because the woman cannot financially weaponize a kid against you if you aren't married and not registered as the father.