How to create counter with unique sequence
U have three states so create a mod-3 counter first.
for that first make a normal 2 bit counter. Take both its output, NAND it and connect it back to reset of both the flip_flops. Counter will start from 00 then 01, 10 and when it reaches 11 it will resets itself (for active low) and start from 00.

Now you a mod-3 counter. Next step is to design is combinational circuit for each bit. Counter outputs should be to combinational circuits.

Take bit by bit. Your sequence 001, 110, 010. Take LSB fisrt, it is 1 only in first state. Counter output is input of combinational circuit, so design a logic circuit that will give 1 only for the input combination 00 (single NAND Gate). Use the same method to design other two bits.