In the Ottoman world around the same period there wasn't really an equivalent to European peerage systems and succession laws. For the Sultan's succession up until the 17th century meant that the rival claimants to the throne would have to kill each other until the strongest prevailed. This was either through open civil war or assassination. There was a shift in the 17th century where the eldest son took the throne, and then his younger brother, and on down the line. Comparatively speaking, no matter how old you were being a son of the Sultan was extremely dangerous for quite a while.

Other Ottoman elites did not have hereditary titles or claims on land (officially), as in theory all land was owned by the Sultan and the timar holders, or tax farmers later on, merely had the right to use the land. The grand vizier controlled appointments for other government positions like military commands, provincial government titles, or palace positions in the capital. Ottoman elite dynasties like the Sokullu or Peçevi tried to become grand Vizier or spread their family members into as many positions as possible to expand their power base. I have not come across anything where birth order was important to who got what as an official custom, although I would imagine it played a role.