I have often come across the claim that the Ottomans received their lands through some sort of grant from the Seljuqs of Rûm, usually from Kayqubad the Great. The assertion is based on Ottoman court historians who wrote several centuries after the events they describe and forged documents akin to the Donation of Constantine in the West. A collection of reliable secondary sources on the subject follows with wikilinks added.
In the works of their later historians the Ottomans, the Karamanids, the dynasty of Aydïn and probably others lay claim to investiture by the Seljukids, generally through a certain 'Alā' al-Dīn, of whom it is difficult to know whether he is the great Kaykubādh or Farāmurz, the last of the dynasty. This is of course to some extent a stock explanation, and it was not to Seljukid investiture that these men owed possession of their territories. Nevertheless, even though the surviving deeds are spurious, there is no reason to doubt that these chiefs sought to legitimize their possessions, for example by homage to 'Abu Sa'īd in 1314, against such rivals or suzerains as were closer at hand.
Claude Cahen, Pre-Ottoman Turkey: a general survey of the material and spiritual culture and history c. 1071-1330, trans. J. Jones-Williams (New York: Taplinger, 1968), pp. 313-14.