I don't remember how I got this quest but it was there among one of my quests so I decided to complete it.
Am not really keen on making pacts or joining the daedric princes except a few so I decided to kill all its cultists.
Then insted of the quest failing or something it stayed there and Beothiah's avatar appeared and I couldn't complete.
I did read UESP wiki since I go there if I get stuck and it said the quest not failing or proceeding was a bug.
Long story short, I used consoles to jump tot he end stage and killed its champion and finally the quest ended with me being its new champion.

My main question is UESP wiki says something about killing the Jarl of Solitude but I didn't get that objective ( http://www.uesp.net/wiki/Skyrim:Boethiah%27s_Calling )
Can someone tell me did something go wrong or is there an error is UESP.
Also will this quest affect any other ?

Really wish Bethesda gave us an option to just kill all members of a group if you didn't want to join them.

Most likely the Jarl bit stated in the wiki is some quest stage that didnt make it into the game
but it might be possible to achieve it in your quest log by using the setstage command

I finished the quest yesterday without any weird bugs or anything and it also ended after killing the champion

I didn't sacrifice any of my companion when they asked me to. Instead I killed them all. I thought this would cause it to fail but it didn't.
So had to use setstage.

Oddly enough I think you're the second person on this board that tried that. Sort of funny but in that quest, once you kill a companion, you're told to kill all of the other disciples. It's obviously a bug where the game can't resolve something internally because you didn't kill a follower in the previous step. It'll probably get patched at some point. I wonder what would happen if you sacrificed a companion after killing all of the other disciples...