You seem to have two ideas in your post: (1) resonant frequency, (2) capacitance. For the first, we usually want an inductor to behave mostly as an inductor. If we operate it at a large enough frequency, then it stops being mostly an inductor. If the resonant frequency is 100 kHz, then you would normally want to operate it at a frequency lower than that. It is not clear to me why you think your inductor would not work correctly at a frequency lower than the resonant frequency.

For the second, a capacitance is present whenever two conductors are separated by an insulator. An inductor is usually in the form of a coil. In between the windings of a coil, there is a parasitic capacitance. The core that you mention is not in between the windings of a coil. So it seems that you are not interested in the capacitance in between windings but in the capacitance that goes across the core. Is this correct?

If you respond to my comments, then perhaps this question can be reopened.

Yes i am interested in the capacitance between the windings.How can we make it bigger?