Is it possible to digitize small signal with large noise?
I may place an input amplifier with K = 10000. So, my small signal will be in the range of ADC's input. Input amplifier will clamp 50 Hz noise to acceptable input levels of ADC and introduce harmonics with frequencies 50 Hz and higher


No. As soon as you allow the amplifier output to clamp, the game will be over. You are trying to dig out 100&nbsp;&mu;V of noise from 100 V of interference. Only 1ppm (part per million) offset in your interfering waveform is equal to the full range of your input signal. Any non-linear operation will mix the interference down into your baseband, and swamp it.

The one thing in your favour is that frequency separation between your wanted and unwanted signals. The first thing you need to do is use a strictly linear, by which I mean passive, filter, to reduce the amplitude of the interference. Ideally, you'd reduce it by a factor of more than 106, but that's not going to be possible with only a 30 Hz to 50 Hz ratio. You may have to sacrifice some signal amplitude at the top end of your 30Hz to get the 50Hz down. Do not even think about active filters, they do not have the dynamic range.

Start off with a high order LC elliptic filter design. This will need large values of inductor as the cutoff frequency is so low. However, the low frequencies will allow the values to be very high tolerance, necessary for getting the pass and stop bands in the right place. Ferrite based inductors can be non-linear, you may  need to under-run them significantly, and test the effect.

Once the interference has been reduced to within an order of magnitude or two of your signal (I think 80dB reduction, a factor of 104, ought to be possible with an LC elliptic, leaving you 'only' a factor of 100 to go), then you can digitise, using a lot of over-sampling with respect to your 30Hz wanted bandwidth, and then recover your signal with digital filtering.

I'm making some reasonable (to me) assumptions about the noise, your requirements for signal fidelity etc in throwing these figures around. Once you've updated your question to include more detail, my numbers may have to change slightly. It's how I'd go about the task though.

(edit) On reflection, there is no way this is going to work. If the 50 Hz interference was absolutely clean a pure, then it would be possible to build a suitable filter and ADC. However, it's going to have phase noise, which will spill over into the signal bandwidth, and probably be sitting on some additive noise as well. (/edit)