Actually we don't know of any Targ bastards. Dany is the only known living Targ after Aemon's demise. But since the dragon must have three heads, we surmise that there are more Targs, half-Targs, false Targs, and ******* Targs out there.
There is conjecture on Aegon's existence. The best hypothesis is that he is actually Young Griff. On the other hand, Young Griff may turn out to actually be a mummer pretending to be a Targ. Other possibilities for current aliases for Aegon include Quentyn, Sarella, Alleras, Jon, Aurane Waters, and Gerold Dayne... and these have either been disproven or are flimsy at best.
I think most people agree that Jon is an extremely likely candidate to be Rhaegar's son, either legally or naturally.
Other than Aegon and Jon, there are no strong candidates... there is only guesswork, supposition, and hope. Writing any more on this subject for you is like the blind leading the blind.
I personally champion Tyrion as a Targaryen *******. I think he's a fun guess. I feel there are a few passages that could be interpreted to say Tyrion is a Targ ******* if you wanted to interpret them that way. I think GRRM will throw us a major plot twist in his story. I very much want to believe that he might inherit the throne.
Varys is fun to speculate about, but other than his name there is nothing.
As for Cersei, Jaime, and the others, there is less proof than for Varys.
