Assuming his potential's the same as Trunks rather than his hax main timeline self, he'd act as a good training partner to Trunks and help him out against #17 and #18. Goten would also be the one sent back in time to Mecha Freeza's arrival in order to see what his father was like. With them becoming far stronger than Trunks' canon pre-Rosat self due to this, however, #17 and #18 would stop messing around and kill one of the two. For a more interesting scenario, I'll say Trunks is the one to die and Goten goes back in time.
Things go the same up until the Rosat trip, in which Goten trains far more actively with Vegeta due to not being interested in getting to know him. When facing Cell, Goten uses Grade 3 as soon as Cell tries to absorb #18, but quickly becomes aware of its flaw thanks to Vegeta and the battle goes a lot quicker than in the canon events. The Cell Games go the same up to SPC's arrival and Goten's death, as Vegeta wouldn't be angry due to it not being his son and instead, Gohan defeats Cell in a typical battle. Things then go the same as in canon.
Vegeta would be far more reluctant of accepting his family due to having not spent time with Future Trunks in this scenario, though would still be changed somewhat by those 7 years leading up to the Boo Arc. With Goten being older and already being nearly Trunks' equal in the Boo Arc, this Present Goten would be stronger than him and win the Kids' Division. He also wouldn't go along with Trunks as his lackey like his canon self, so the Mighty Mask events don't happen. I believe this change in personality would also affect their fusion as well, with this Gotenks being more serious than his main timeline self due to Goten's personality being far less submissive to Trunks' arrogant nature. When fighting Boo in the Rosat, they wouldn't mess around and would destroy him as a SS3. Because of this, Goku isn't revived, nor is Vegeta.
As for Super, Beerus would still wake up after having his SSG dream due to the task not being impossible when 6 Saiyans were still living. Without Boo, Beerus would leave the party satisfied, though soon return in order to ask about SSG. The Dragon Balls would be used to transport Bulma to Namek, at which point she'd use their DBs to revive Goku and Vegeta so the ritual could be performed before returning to Earth. Things then proceed as in the main timeline, with the main change being this Vegeta is far more disassociative with his family. The events of the series still happen as in canon up until the Future Trunks Arc, in which Goten takes Trunks' place. Other than that though, things proceed the same from there.
That is, until the Moro Arc, in which Jaco would instead be sent to Earth to request Goku and Vegeta's aid. Without Boo restoring their Ki or proving a distraction to Moro from them for a while, however, they'd ultimately lose to him and he'd continue his path of destruction until Whis or Beerus deemed it as appropriate to get involved.