I need a device (Device A) that connects to my WIFI Network (Device B) through WIFI and when I connect to (Device A) using WIFI or wired it assigns me different IP address using it's DHCP configured by me. Please list the devices.
Not going to be easy to find. What you want is a router that will accept wifi for its WAN. There are some routers but most i know of are rather old models. Maybe one of the newer repeater/extenders has this feature I do not follow those devices much.
You could load third party firmware like dd-wrt on a router but you need to solve the issue of only have 2 radios. You could build your own by using a wifi bridge and hook it to the wan port of a router.
The Engenius wireless bridges can do what you want. I would bet so can the Ubiquiti. I have use the Engenius ENH202 (now discontinued) when my ISP disconnected me in error. I used the Engenius, fed from an agreeable neighbors' WIFI. Used it in router mode which took WIFI as the WAN and had all the standard NAT and DHCP functions of a router.