It’s bit lengthy but I think I need to do an introduction:

Two years ago I took a job and got a contract with a certain salary that at the time seemed ok. I wasn’t sure about how much I should ask at the time (plus I was moving from my home country, which has different salary expectations) and, overall, I wanted the job and wanted to move here, so I accepted the offer.
I got a good raise after 1 year I was here (20%), and got my contract renewed. Though in the meantime I got to know that other people who have started in my company with my same position, got an initial offer that is higher than my initial salary combined with the raise I got after a year.
I subsequentially asked for a new raise which was initially denied due to the fact I already got a raise a few months before. I therefore told my manager I was aware I was getting less money compared to my colleagues who started later (not sure if that was unprofessional(?)), and I asked whether that was due to them having better skills, and if that was the case to help me understand and give me a feedback on which gaps I needed to fill.
They weren’t able to tell me anything or point to anything that they are doing better (also because they never asked my supervisor about my performances), but agreed to give me a small raise (I’m still getting slightly less though). The topic sort of dropped at the time also from my side due to a couple of other personal reasons.

Now, I’m about to start my third year here. I wanted to bring up the topic once again, because ultimately I’m not happy with how much I’m getting, plus I feel my work is not appreciated enough since in my opinion I’m doing a pretty good job. I feel like I would like a 20% raise compared to what I’m earning now, which seems a lot, but would actually be only an average salary for a professional with my experience in my industry. 

I’m prepared to leave eventually if I don’t get it and got other job offers recently. Of course I would prefer to stay where I am now, but this situation is making me feel very frustrated at the moment.
Do you think it’s fair my employer reasoning? (That compares my raise in percentage to my salary, to which 20% is a lot, rather that the industry average salaries, to which my salary is low)
Or it’s my fault to have accepted such a low salary when I started?