I am unsure about Hinduism and Jainism spreading this far outside India, especially where there are other religions' influence.
Manicheanism is possible as it was already prevalent in Central Asia, Tengrism was the religion of the Turks, Buddhism was widespread, Christianity will be strong among the Volga Bulgars, Tatars and probably the Bashkirs(who otherwise will be Pagan/Tengrist or Buddhist), Tao? Maybe, maybe not. As most Turkic people live faraway from Core China.
My bet is probably Christianity that spreads first to the Volga Bulgars and then the Tatars, then to the Chuvash and the Bashkirs and then to other Turks in the Central Asia. Possibility with Christianity is if the people bordering the Byzantine Empire join it after converting, the whole migration patterns of others would be different.
'Hinduism' spread further north in some ways than Zoroastrianism (in Persia, geographically the region of south and southwestern Iran). Several Kushan emperors sponsored the gods of Hindustan and adopted heavily the traits of the Hindu both in religion and in naming custom. Almost all Kushan emperors claimed to be firm in the Dharma and of friendship/rule over the Aryans. Vasudeva I for instance, claimed on his coinage to be the servant or ally of Shiva. Hepthalite rulers were similar, promoting the Hindu gods to the far north of Central Asia and adopting through their heritage of Kushanshah lineage, the Indic characteristics that had been en vogue among the peoples of Central Asia after the advent of the Silk Road, under the Kushan empire. Zoroastrianism by contrast, was the state religion of the Sassanid royalty and not of its populace and certainly not of the nobility, who practiced Iranic polytheism or at least a type of Zoroastrianism, which excluded Ahura Mazda.
Manichaeism and Nestorianism are possibilities certainly. So, we have the answer generally, regarding religion:
-Iranic paganism: A Turkic entity perhaps who attempts to connect itself to the Arsacid past and to the more ancient and mythical notions of the Eranshahr. Say, the Ashina clan instead of their flight to the Volga, invade the Sassanid empire and defeat the armies of Hormizd IV. From here, the Ashina form a ruling coalition with either the Mihran or Karen family and we see the restoration of a new dynasty of Eranshahr, say the Ashinid empire.
-Zoroastrianism: The less likely position, the Turkic entity in Iran appropriates Sassanid religious structure instead of appealing to the noble houses.
-Nestorianism: This can be achieved in Central Asia or in a conquest of Iran. I would imagine it being more likely in the case of Central Asia. Nestorianism while somewhat strong in Mesopotamia, was not necessarily ascendant, at least not as much as some thinkers have deduced.
-Manichaeism: An interesting option, the nobles of Iran may even be receptive to this religion if presented well. Regardless, it is effective in Iran, Mesopotamia and within Central Asia. Though, I know of no real presence of Manichaeism in Hindustan, it may also be a religion that can appease some of the Indus Valley folks.
-Altaic polytheism: The most obvious option, remained their religion generally, until the Abbasid began using Mamluks and thus associated the Turkish peoples more and more to Islam and Arabo-Persianism. This is feasible technically anywhere and will allow a more flexible ruling system wherever they find themselves.
-Buddhism: A strong contender, for Central Asia, Bactria, India, etc... It has obvious benefits and historically was quite strong in these areas prior to Islam. Could also be received well by the Iranian noble houses and possibly by the denizens of the Pontic steppe or Northern Eurasia, such as the Slavs or Balts.
-Hinudism: The option would be plausible in the route of a 4th Kushan empire in the model of a Turkic Hepthalite empire, allowing Hinduism to spread north more easily. This also allows the Turkic peoples to associate to Hindustan more easily than otl. Though, in otl, without even relations, the Turkic states empowered by the wider Islamic world, conquered almost entirety of the Hindu world.
