painting entrance
Great-Great Grandpa Riddle (or GGGP) is the logical thing to call the partner of Great-Great Grandma Riddle (or GGGM), a man seen standing beside her in a painting at the start of Secret Movie.
Yadina Riddle pointed at the painting and said "our very own great-great grandparents", with Xavier Riddle elaborating that "they build the whole museum together" referring to The Secret Museum.
This appears to be the same man seen in a painting on the wall in many episodes, which the kids use to enter the Secret Museum hidden underneath the Riddle Museum, which is open to the public. In the movie, this painting is replaced with a painting of the grandma done in a similar style: seated in a chair with a pet and wearing period clothing.
It is not 100% certain that his name surname would actually be Riddle, though that would be likely if they were married: it is not explicitly stated that the Riddles siblings' GGGM was married to their GGGPA, but that would be common practice going back four generations to a previous century.
This man bears a strong resemblance to series creator Brad Meltzer who Brad Meltzer (character) is based upon. This can especially be seen in the adult version of Brad who is seen near the end of the Secret Movie attending Yadina's inauguration. The only difference seems to be that adult Brad has some visible short hair, and is not completely bald (or shaven-headed).
Also resembling GGGP and adult Brad is a man briefly shown at the end of I Am Eleanor Roosevelt. He resembles GGGP more since he is fully bald and doesn't have visibly short buzzcut hairline.
During I Am Charlie Chaplin, there is also a similar-looking bald man in the audience watching Hannah Chaplin sing.
This man appearing in different time periods could be explained by him having similar access to time travel as the Riddles do now, and which their GGGM previously enjoyed.
In I Am Zelia Nuttall, Xavier is given a puzzle belonging to his great-great grandparents for his birthday, and it has their picture inside it.
In I Am Esther Martinez, it is revealed that he and Great-Great Grandma Riddle started the museum with nothing more than a trunk filled with family antiques.
He had a son[]
I Am Rukmini Devi shows photos of him and his wife together and reveals they had a son.
No other children are shown, so presumably Yadina's great grandma was that son's wife.