Alright, this isn't a very educated question, but I'll humor you because you are most likely unfamiliar with the way things work (transferring account mods in between consoles).
Lets take 3 well known games into comparison with Call of Duty : Black Ops 3; Call of Duty : Ghosts, Call of Duty : Advanced Warfare, and Grand Theft Auto V. All of these games are on both Last Gen, and Next Gen consoles, However Call of Duty : Black Ops 3 lacks one key feature that all the other mentioned games have.... Cross platform account transferring. COD : AW and COD : Ghosts both have the call of duty account feature, where you can link all your consoles to one account and share stats, so u can level up your character on whatever console you choose. GTAV has a similar feature, 'Social Club' which allows the user to upload the account statistics from one console to another to another and so forth. Back to the point, COD : BO3 lacks any kind of account link feature... no call of duty account login, no social club, no nothing, due to the games development focus on Next Gen consoles, Old Gen support for these sorts of things has been dropped. So what this means is that, Call of Duty : Black Ops 3 for the ps3/xbox360 and the ps4/xboxone are completely separate games, and don't include any kind of stat transfer system.
In short, the reason your modded ps3 stats aren't transferring to the ps4 is because its impossible to do so, as there is no way to link your ps3 account to your ps4 through BO3.