The Sage of the Six Paths had Rinnegan in both in his eyes. He also awakened a third eye on his forehead.
Is that a Sharingan of some kind?
What powers does that third eye grant it's wielder?
From the Wiki
After awakening his Rinnegan, he also manifested a red circle marking with two ripples patterns in the centre of his forehead, seemingly a byproduct of his ultimate dōjutsu manifested alongside his senjutsu training.
It references episode 426 of Naruto Shippuden and suggests it wasn't a true eye but rather a marking. There's no way to be sure if it gave him any special powers, but all
abilities he exhibited were in line with what we know was possible via his Rinnegan / Mangekyo / Senjutsu abilities so it doesn't seem to have given him anything.
Additionally it's flat and lacks the depth that Kaguya's third eye had, also suggesting it was simply a marking. The best theory I can come up with is that it was an incomplete manifestation of Kaguya's third eye.
Actually, that marking is the Mangekyo Sharingan. When Hagoromo and Hamura (both sons of Kaguya Otsutsuki) fight Kaguya, Hagoromo has to kill his brother for he was under the control of Kaguya. But thanks to Gamamaru (presently the great toad sage), Hamura was saved by sage power.
Immediately after this incident, Hagoromo awakens his Rinnegan and also his Mangekyo Sharingan. He also thanks his mother (Kaguya) for she was only responsible for the awakening of his Rinnegan and Mangekyo Sharingan.
It is the Mangekyo Sharingan. When Hagoromo "kills" Hamura and gains his Rinnegan, he also gains the "third eye." It doesn't really look like an eye, but more of a marking representing the Mangekyo Sharingan. When Sasuke gains his Rinnegan, his Rinnegan manifest in his left Mangekyo Sharingan eye. In Sasuke's Rinnegan, there is tomoe which shows when he is at full power and that there used to be a sharingan in that eye. It also shows that he still has the power of his left Mangekyo Sharingan. Though an issue with this hypothesis is that Madara did not have tomoe in his Rinnegan and did not get the Rinne Sharingan till late in the series. And I'm pretty sure he still had the power of his Sharingan, even when both his eyes were Rinnegan.
In all, the red mark probably represents the Mangekyo Sharingan in order to show that Hagaromo has both the power of the Sharingan and the Rinnegan.