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In this paper, we study common zeros of the iterated derivatives of theEisenstein series for $\Gamma_0^+(N)$ of level $N=1,2$ and $3$, which arequasi-modular forms. More precisely, we investigate the common zeros ofquasi-modular forms, and prove that all the zeros of the iterated derivativesof the Eisenstein series $\frac{d^m E_k^{(N)}(\tau)}{d\tau^m}$ of weight$k=2,4,6$ for $\Gamma_0^+(N)$ of level $N=2,3$ are simple by generalizaing theresults of Meher \cite{MEH} and Gun and Oesterl\'{e} \cite{SJ20} forSL$_2(\mathbb{Z})$.

On the common zeros of quasi-modular forms for $\Gamma_0^+(N)$ of level $N=1,2,3$