A misc quest to find copy of "Fragment: On Artaeum" is broken.

i already have that item when the quest triggered, cannot turned in the item, so anyway attempt to follow the quest, go to that quest spot, but cannot find the item.

patch 1.4

Have you tried putting the book in the chest there and then taking it out again?

In the console type...
player.drop 0001AD06 1 (and press ENTER)
Close console. You should now be able to pick the book up and continue.

@JMC002 You can't normally remove quest items, so the game won't let you put it back into the chest.

you can't move/drop/store quest item. so, no. can't do that.