“but its not the same hat worn in Yehsivas. It seems similar to a hat the Famous Rambam Pictures have”
Actually, your dead wrong (over and over).
Again, Chacham Ovadia Yosef along with all Sefardim wear REGULAR black hats that are worn by all Yeshiva bochrim and avrechim in Eretz Yisroel.
He wears the clothing that the Sephardic “Rishon Letzion” wear only by his drashos, simchas, and when he appears in public. When he davens he wears a regular black hat like any other Rosh Yeshiva. His children wear the same hat as he does.
http://www.theyeshivaworld.com/photos.php?albumid=5518867748688102977&photoid=5518868176361218226
Collection of Photos On 90th Birthday of Chacham Hagon Rav Ovadia Yosef Shlita
http://www.theyeshivaworld.com/photos.php?albumid=5518867748688102977&photoid=5518868034512234546
http://www.theyeshivaworld.com/photos.php?albumid=5518867748688102977&photoid=5518868067967794690
http://www.theyeshivaworld.com/photos.php?albumid=5518867748688102977&photoid=5518868264814422978