If I am not wrong here. You have about 180 LSB(least significant bit) in noise peak to peak. That is very much in a 14 bit system. Using a battery as source. I do not know your system. But I would have expected way better performance. What is ADC converter range in volt. In this setup? As your system is now it is pretty much useless for doing any analog to digital conversion. Assuming your board has a range +/- 2.5 volt. I would have expected to see some in the range of 4915 (ish) then connecting to a good and fresh 1.5 volt battery. Check switch S20 to 23 and the voltage on pin 3 and 5 U1. You should see 2.5 volt in these pins then the internal references are used. The error could be that the reference inputs are floating

 

Thank you very much for your accurate answer. Indeed, the ADC range as you asked me is +/- 2.5V. I tried with a battery but this battery was regulated. that is the reason why it was so noisy. It is effectively better with a real battery. You are right concerning the switchs S20 to S23. They are all open.
I have a proper voltage on pins 3 and 5 of U1.

 

If S20 to S23 all are open it is something wrong here. S21 and 23 should be closed. S20 and S22 should be open. Attention to details are important here

 

There is an automatic 2V Vref if nothing is connected but connecting S21 and S23 allows the Vref to be more accurate. I have done so but the signal is the same. All the C1, C2, C3 and C4 capacitors are connected as well with 220pF.

 

I will open a new post as the things have changed. Indeed, I have used a different generator to power supply the acquisition board without the AOPs. I do not have any more these problems. Thank you for your help, I am waiting for you on my second post.
Wishes