Jim passed on his job at the GCPD when you became of age he took you with him to work and started training you up himself in hope that Gotham would always have a detective Gordon
His hat when you were a kid you use to steal it from him and wear it around the apartment until one day Harvey gave up on trying to get it back and aloud you to have it
His umbrella when he went into arkham he asked jim gordon to give it to you "no matter what happends to you jim Y/N must get it understand" Jim couldn't understand why until he realised how much of a sentimental thing it was to the pair of you , that and the knife hidden inside