Could you please explain me this question. As we know that every field has a source like electric field has electric charge and magnetic field has magnet etc. So what is the source of the Higgs field?
The Higgs particle is an elementary particle in the standard model of particle physics
All elementary particles have a meaning in the quantum mechanical framework, not the classical that you are discussing.
In quantum field theory, every particle in the table above is a quantized field which covers all spacetime. Creation and annihilation operators define the sources , for example a creation operator creates an electron, acting on the electron field, or a Higgs particle creation operator acting on the Higgs field creates a Higgs meson.
Good question. The Lagrangian of the Standard Model of physics is constructed in such a way that the standard answer to your question is: the Higgs field itself. This is because it contains a huge self-interaction term $\lambda\phi^4$ that causes the ground state of the Higgs to correspond to a constant nonzero value. However, the existence of such a term has not yet been established experimentally and there are other possible explanations for the Higgs vacuum expectation value (which definitely IS established) that do not involve self-interaction.