Interpolate DFT Coefficient of a Frequency That Is Not in the DFT Bin
If you need very specific frequency you should either use the Discrete Fourier Transform (DFT) definition or the Goertzel Algorithm.

Yet, if you need higher resolution Grid, you can use many off the shelf algorithms to interpolate.
The native Interpolation Kernel would be the Dirichlet Kernel since it is the Sampling Kernel for the DFT.
An easy way to interpolate the grid in the Frequency Domain using the Dirichlet Kernel is by Zero Padding of the signal in the Time Domain.
As this is equivalent of higher rate sampling of the Discrete Time Fourier Transform (DTFT).