Thief's Cognitite Shards can be obtained through promos and Tasks. You can use them from [Bag] to exchange them for certain Phantom Thieves' Cognitite Shards.
In addition, collecting 60 of a Phantom Thief's Cognitite Shards will allow you to exchange them for a Cognitite, which is used to Awaken the Awareness of that Phantom Thief.
※ Please note that Cognitite Shards and Cognitite will not allow you to acquire that Phantom Thief. They can only be used to strengthen Phantom Thieves that you already own.