Processing 47-53 MHz signal sampled at 96000 Hz
In short, what you're trying to do is impossible. The technique is known as band-pass sampling, or undersampling, but for it to work, you need that the signal's bandwidth be less than half your sampling frequency.

When you sample a signal with spectrum $S(f)$ and bandwidth $B$ at sampling frequency $f_s$, the sampled signal has spectrum $$S_s(f)=k\sum_i S(f-if_s)$$ where $k$ is a constant. If $B&gt;f_s/2$ then the replicas $S(f-if_s)$ overlap and you end up with a distorted spectrum.

You are correct that the highest frequency bin in your FFT is 47906.25 Hz.