Co-parenting

[MommaManchester]

Can my ex take me to court to have sole custody?

Your ex can try. Doesn't mean they will get it. Courts often remain with the status quo unless clear rationale to change.

Are you in the uk? He can try but he would need a very very good reason to succeed such as prolonged and proven abuse of the child on your part or something equally serious.
Unless there is a massive backstory, I doubt he will succeed.