you can only find the Beloved disciple referred to in the writings of JOHN , this as John, the way most people see this is John, himself is boasting that God Loved Him more than the other disciples, just as I would boast that Jesus loves me more than he did John. But God Is not a respect of persons There would not have been a dsicilpe that was loved more than the other disciples. But Peter was a beloved, matthew was a beloved disciple and I am a beloved follower. since when did "beloved" mean most loved, it is just a saying that we are loved so John was Loved, just as I am loved.
Webster 1828
BELOV''ED, ppr. [be and loved, from love. Belove, as a verb, is not used.] Loved; greatly loved; dear to the heart.
so all John is saying is that Jesus Greatly loved him, man has put it that Jesus had respect for John more than the rest, but this just can't not be. yeah I know someone will ask about Esau, God hated Esau because without faith it is impossible to please Him, Esau sold His birth right for a bowl of beans he had no faith in God to take care of him.
Ro 2:11For there is no respect of persons with God.