The only story in which the Master appears and is called 'Koschei' is the Virgin Missing Adventure The Dark Path.
In this story, featuring the Second Doctor and set over 200 years after the Doctor left Gallifrey, the Doctor comes across a man calling himself 'Koschei'. He does not know who he is, as 'Koschei' is a new alias for the Master.(Just as he will use other aliases such as 'Kalid' or 'Victor Magister' later on.)
The BBC Past Doctor Adventure Divided Loyalties features the Fifth Doctor, and is set during Season 19. The main antagonist is the Celestial Toymaker. As part of the Toymaker's schemes, he lures the Doctor and his companions into his Dreamscape. Here they experience a series of nightmares based on their own pasts. Adric dreams about his past, in a way that totally contradicts "Full Circle". Nyssa dreams about her past in a way that totally contradicts "The Keeper of Traken". Tegan dreams about her past in a way that totally contradicts what we have learned about Tegan in other novels.
The Fifth Doctor dreams about his time on Gallifrey. The Doctor at the Academy is clearly the Fifth, rather than the First, Doctor. Strange dream-like events occur, such as Type 35 TARDISes becoming obsolete before Type 30s have even been launched. Mortimus is at the Academy with the Doctor, is his close friend, and leaves Gallifrey before the Doctor. And it is explicitly stated within this dream that only someone with a Rassilon Imprimature can regenerate, operate a TARDIS, or even travel in a TARDIS. Only the Time Lord High Council can give out these Rassilon Imprimatures. It is also explicitly stated that the Doctor never got one. To say nothing of the various companions the Doctor has had over the years. This all takes place in a Chapter explicitly entitled 'DREAMING'. Before the sequence, the Doctor is said to fall asleep. Shortly after the sequence, the Doctor is said to wake up. One of his first remarks is on the "weird nightmare" he has just had. And the Celestial Toymaker later confirms that this was a dream that he created to torment the Doctor. This dream sequence does feature a character called 'Koschei', who the Doctor knows well. However, this completely and utterly contradicts The Dark Path. Just as the entire dream sequence, were it to be seen as a literal depiction of the Doctor's days at the Academy, would contradict every other Doctor Who story ever, including the non-dream parts of Divided Loyalties.
So, the only story where the Master appears and is called 'Koschei' is the Virgin Missing Adventure The Dark Path.