The short answer is no. You can´t make them work under normal circumstances. The PS4 is not compatible with the old accessories and add-ons of the PS3. So in theory, all the sticks from that era are useless.
Can I use PS3 arcade stick on PS4?
If you are getting the PS4 version of Street Fighter 5, you will be happy to know that some PS3 arcade sticks/controllers will be compatible. ... First of all, you need to keep the DualShock 4 on (at all times) so that your PS3 stick/controller can be paired up with it.
Can you use a FightStick on PS4?
Plug the USB from the Fight Stick directly into your Playstation 4 (the compartment is located on the left side). Next. Using the 2-4 ft USB capable that came in the box. Connect it to the front of your fight stick, & the other end into a Sony® Playstation 4 controller.