postgeniture

from The Century Dictionary.

• noun The state or position of a child born after another in the same family: used specifically of the second born of twins.

from the GNU version of the Collaborative International Dictionary of English.

• noun rare The condition of being born after another in the same family; -- distinguished from primogeniture.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun The fact of being born after someone else of the same bloodline.