Not just Jackson. IIRC, Lincoln carried an arrest warrant for Chief Justice Roger Tanney in his pocket for about six months, "just in case."
No, he gave it to his errand boy, political factotum, and personal security agent, U.S. Marshal Ward Hill Lamon, as recounted in Lamon's postwar memoir.
Lamon kept the warrant for a while, and then, when Lincoln did not follow through, apparently disposed of it on his own as stale-dated.