The first thing I would do is look through your sister's DNA matches at Ancestry. You need to find 1st or 2nd cousins who don't also match you. The chances of someone who is a 1st or 2nd cousin on your mother's side not having a DNA match with you is essentially nil, so anyone who matches your sister at that level and not you is likely a descendant of her father's parents or grandparents. The ones that match both of you are descendants of your mother's parents or grandparents.
Once you've found these matches (if there are any) you need to look for their trees and then try to find likely candidates for any male relatives of the appropriate age who might have been in the right location at the time your sister was conceived. If those matches don't have trees available at Ancestry then you might consider reaching out to them for more information. Bear in mind that there is a reasonable chance that her father is still alive and that this could well be a very sensitive issue. I personally find that providing as little information as possible in my initial contact with matches seems to work best, perhaps it's less likely to scare them off. Usually just a basic email that you have a DNA match and would like to further investigate your connection.
If you don't find any matches out to 2nd cousin you can look through the 3rd cousin matches at Ancestry, but at this level you will probably be better off, as others have already mentioned, uploading both of your results to MyHeritage, FTDNA and GEDmatch as the tools at those sites are much better suited to investigating matches at that distance. Also be aware that at the 3rd cousin level it is possible for a cousin on your mother's side to match your sister and not you since 3rd cousins have about a 10% chance of not sharing enough DNA to show up in results. Let me know if you need clarification on any of this or would like more help.