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Can Magnetic fields produced by thin current carrying wires with infinitesimal area have curl with a delta function in it ?? As area is Zero current density J definitely becomes infinite at where Wire is located So curl has a delta function in it , Am I right ?Please correct me

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Off hand, I'd think so, for some scenarios: $\vec{r}$ as in cylindrical coordinates, $\nabla \times \vec{B}=\mu_0\vec{\delta}(\vec{r}-\vec{r_0})J_0$. You could probably find some examples of this researching Green's Method solutions to Maxwell's Equations.

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