This just shows that you have strong interference in the analog inputs because of EMI noise. Where it is coming from?
Well, you can read the PCB as schematics, so as Richard said, good luck here!
If you make a lot of ADC readings, say 20, and then sort them in order, through away the 5 first and last numbers, with the rest 10 make a mean number, then you may get rid off the 100nF capacitor and be more confident of the readings. This makes for a low pass filter in software.
Personally, NEVER use raw adc readings. This is just looking for troubles. A spike can ruin your day. Make many readings and get the best of them to be sure of noise free readings.
Ioannis
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