Karma kanda has many yajnas which can give heaven and such other fruitive activities, is there mention of yajna which can fulfill a wish? Are there any rituals, yajnas, vratas, mantras or praying to a specific deity that can fulfill wishes.
There are many instances in the Puranas where people have worshiped a variety of gods to fulfill their wishes. Most of the times the ones invoked are from the Trinity - Lord Brahma, Shiva and Vishnu but there are also instances of the Goddess or some other deity being invoked for the fulfillment of a specific wish.
However, since your question is primarily about Vedic Yagnas, I am sharing the following excerpt from the Shatapatha Brahmana that mentions a wish-fulfilling sacrifice performed by no less that Brahma & his sons:
They went on singing praises and toiling. Then Parameshthin, son of Pragâpati, saw that sacrifice, the New and Full-moon offerings, and performed these offerings. Having performed them, he desired, 'Would I were everything here!' He became the waters, for the waters are everything here, inasmuch as they abide in the furthest place; for he who digs here on earth finds indeed water; and, in truth, it is from that furthest place, to wit, from yonder sky that he 1 rains, whence the name Parameshthin (abiding in the furthest, highest place).
Parameshthin spake unto his father Pragâpati, 'I have discovered a sacrifice which fulfils wishes: let me perform this for thee!'--'So be it!' he said. He accordingly performed it for him. Having sacrificed, he (Pragâpati) desired, 'Would I were everything here!' He became the breath (vital air), for breath is everything here: Pragâpati is that breath which blows here (the wind); and whatsoever knows that it is thus he blows is his (Pragâpati's) eyesight; and whatsoever is endowed with breath is Pragâpati. And, verily, whosoever thus knows that eyesight of Pragâpati becomes, as it were, manifest.
Pragâpati spake unto his son Indra, 'Let me perform for thee this wish-fulfilling sacrifice which Parameshthin has just performed for me.'--'So be it!' he said. He accordingly performed it for him. Having sacrificed, he (Indra) desired, 'Would that I were everything here!' He became speech (vâk), for speech is everything here; whence they say, 'Indra is Vâk.'
Indra spake unto his brothers Agni and Soma, 'Let me perform for you this wish-fulfilling sacrifice which our father Pragâpati has just performed for me.'--'So be it!' they said. He accordingly performed it for them. Having sacrificed, those two desired, 'Would that we were everything here!' One of them became the eater of food, and the other became food: Agni became the eater of food, and Soma food; and the eater of food, and food, indeed, are everything here.
These five deities, then, performed that wish-fulfilling sacrifice; and for whatever wish they sacrificed, that wish of theirs was fulfilled; and, verily, for whatever wish one performs that sacrifice, that wish of his is fulfilled.
The New and Full Moon Sacrifice is also called DARSAPÛRNAMÂSA-ISHTÎ in the first Kands of the Shatapath Brahmana and this seems to be the most clear mention of a wish-fulfilling Vedic sacrifice that even helped Lord Brahma and his sons fulfill their desires.