You don't give any details other than your DNA match to an illegitimate child of a 'probable' 3 x g/aunt which seems odd?
When you say 'probable' does this mean you don't have a birth cert. for her naming her parents which would remove the 'probable' & you don't say if you have a BC for the illegitimate child?
What info. have you & your match been able to verify to link you to the 'probable'?
I don't think you have gathered enough info. to work out the connection or have you just not posted what info. you'd checked?
Only this week on MH (where I don't have a tree, I'd uploaded my data), I found a 3rd-4th cousin match 1.1% (78.2 cM) Shared DNA, 3 Shared segments, largest segment 51.8 cM.
No removes for us as we were born the same era/decade.
His tree consisted of his parents names, neither of which I recognised with only 10 shared matches.
I looked at the surnames listed for some of our shared matches which gave me an idea of which line he was descended from.
Long story short, he was unable to elaborate on his mother's line which I'd luckily worked out was most likely our connection as his father would have (in normal circumstances) descended from the same surname taking it back 1-2 generations & that surname seemed unlikely from shared matches & my own research.
I looked for his mother's death (Scotland) on the index post 1974 which gave me her mother's maiden name, then found the marriage of her parents which I downloaded to get the names of their parents & BINGO!
The g/m of my match was one of several illegitimate children of my 1 cousin 3 x removed.
His gg g/mother was a sister of my gg g/m.
Annie