Alexander is one of the jar people. His questline is long and you need to do two other questlines!!!
Jar Bairns questline
Diallos questline
The whole questline starts at the beggining area of the game, Limgrave. You can meet Alexander on top of the cliff next to the bridge close to the Summonwater Village Outskirt Site of Grace. You can find Alexander stuck in the ground asking to let him free. He tells you to hit him hard on the back to get him out so hit him on the back hard. Hit him hard on the back with a weapon and he will get unstuck (Alexander will not take damage in this encounter by any means). By getting Alexander out he will give a emote (or whatever it's called and i actually don't know if Alexander will give you an emote but I think he does, but you should still save him :D).
After that encounter you can find Alexander in the Gael Tunnel, located to the side of the boss fight "Magma Wyrm" (But not to the side of the boss fight, next to the boss fight door). He tells you that he wants to go to Redmane Castle.
After that encounter you can find Alexander in the yard of Redmane Castle if triggered a , then above Jarburg in Liurnia. In Jarburg he will tell you to knock him loose AGAIN now using a oil pot (A craftable item. It is craftable item only when you have acquired Nomad's Cookbook 17). After that he can found in Seathewater Terminus and Talk to Alexander ( Alexander is in the lava near Seathewater Terminus). In the Mountaintops 0f The Giants you can Summon Alexander for Fire Giant boss.
After that make your way into Crumbling Farum Azula where he challenges you to a duel. He can be found near the Dragon Temple Lift Site of Grace. go past the plaza full of undead up the flight of stairs, turn right and you'll see two square bracket shaped archways. Jump on the archway on the left (closest to the sleeping dragon) to get over to the other side. Alexander can be found directly on the flat arena after crossing the crumbling tower. Beat him and you will recieve Alexander's Innards and Shard of Alexander, if you lose nothing happens.