In social networks, different users may have different privacy preferences and there are many users with public identities. Most work on differentially private social network data publication neglects this fact. We aim to release the number of public users that a private user connects to within n hops, called n-range Connection fingerprints(CFPs), under user-level personalized privacy preferences. We proposed two schemes, Distance-based exponential budget absorption (DEBA) and Distance-based uniformly budget absorption using Ladder function (DUBA-LF), for privacy-preserving publication of the CFPs based on Personalized differential privacy(PDP), and we conducted a theoretical analysis of the privacy guarantees provided within the proposed schemes. The implementation showed that the proposed schemes are superior in publication errors on real datasets.