I now see that you are trying to include two constraints on one line, separated by a comma.
Your first attempt, norm(p0,1)=norm(X,2)^2/10, is an illegal expression assignment.attempt.
Your second attempt, norm(p0,1) == norm(X,2)^2/10 is a nonlinear equality constraint, which is non-convex and violates CVX;s DCP rules, hence the error message you received.
The last version you show, norm(p,1) <= norm(X,2)^2/10 is convex and acceptable to CVX. it is different than the non-convex equality constraint.
The sum of p can be constrained to be a constant with the constraint sum(p) == your_constant. DO you also want a constraint on the *one) norm of p? If so norm(p,1) <= some_constant is convex and allowed; while norm(p,1) == some_constant is non-convex and is not allowed in CVX.
If you really want the non-convex norm equality constraint, either use a tool which allows non-convex constraints, or try the approach provided in @stephen_boyd’s answer at How to handle nonlinear equality constraints?