Illegitimate

[Biggles50]

You seem to have the appropriate documentation in the Court record. 

Did the Court find him the Father and issue a maintenance order?

If they did then in reality that is almost as good as it gets.

Then DNA can prove his lineage to an extent with the extent being direct descendants of him taking a DNA test and you matching them.

Which in itself may result in a waiting game or if you find relatives who then respond to contact and asking them if they would be willing to take a DNA test.

In your shoes I would take a guess at one of the options and build a tree around them and going back to their Great Grandparents.  Then see if any of your DNA matches who have an appropriate cM DNA can be linked into the tree. 

This is what I have done, there are 700 people in the Irish tree and those who share more than 40cM have been linked into the tree and over a 100 others Shared Matches are Grouped as a WIP.  One day I will find a viable link, so far official documentation simply does not exist.

[brigidmac]

The people showing at the bottom of the thru lines ARE related to you

But as Biggles + others say you have to confirm if the relationships are the ones suggested by thru lines

Where trees differ you have to work out if 1 set of people haveatched on to the wrong Charles BELL

try seeing if you have surname matches to the wife and mother of both Charles BELL. That may give you a  clue to the right person . But if there are no matches you can't eliminate anyone