Does modified Morlet wavelet function satisfy the admissibility condition ?
Do you have any reference for the answer please.
No, it doesn't (at least not in theory). You know that the admissibility condition is
where $\Psi(\omega)$ is the Fourier transform of the mother wavelet $\psi(t)$. If $\Psi(\omega)$ decays sufficiently fast (which is the case for the Morlet wavelet) then the admissibility condition reduces to $\Psi(0)=0$, i.e. $\psi(t)$ must satisfy a zero-mean condition. However, this condition is not satisfied for the Morlet wavelet. So the Morlet wavelet is not admissible, but in practice this is no problem because $\Psi(0)$ is very small.
 M. Vetterli, J. Kovačević: Wavelets and Subband Coding