Are they Cheating you? Not in a technical sense. In a moral sense, absolutely, but not in a technical sense.
First things first: You are always able, within a company, to negotiate a pay rise. Now, the company is under no obligation to humour your negotiations, but then you are under no obligation to continue your employment. If you haven't negotiated for a raise after a year of employment (especially given the recent inflation) - that's on you.
Next: A New joiner is equally able to negotiate their starting rate at the time of accepting the offer. This is usually the easiest time to get a good rate as the company has a distinct need they are trying to fill and you have yet to accept the offer. Some general advice that is often thrown about the Internet is to change jobs every 2-3 years to leverage this phenomenon into the largest salary you can get.
In addition, the new joiner may or may not have additional skills or experience that the Employer might place a premium on - such as knowing a second language or prior work experience or may simply just be better at negotiating than you. That's life, unless you are the undisputed best in the world, there's always someone better than you and even then, it's just a matter of time.
Now, I'll grant you that this situation does suck, at one company I worked at, I started as a new hire and had negotiated myself a very good rate (I had multiple offers at the time and played them against each other) - so I was in the position of your co-worker, I was payed quite a bit more than my colleagues - should the Company have increased their salaries with reference to their years of experience? Probably - but they didn't. Eventually, those staff left (see above, your ultimate bargaining chip).
To address your actual question: How to ask for a Pay Rise:
Firstly you want to make a Business case to them - what value do you provide to them? Not just your assigned duties, but what additional value do you provide? I'm not familiar with your field of work per se - but things like "My typo rate is the lowest in the team, leading to a superior work product" or "I'm consistently in the top N performers on the team".
Next, you want to make a pragmatic case to them "I've been for a year, I feel that my initial rate was reflective of a new starter with no experience, but now the output I'm providing owing to my experience justifies an adjustment in salary" - if your business case is weak (you aren't a top performer or you have no additional responsibilities), then here is where you can add some weight to your argument - talk around the issue, perhaps bring up the high inflation rate of the last year, or if you know your company did particularly well the last financial year.
Finally, you want to set out some expectations:
"Based on my performance in the team and my experience with the company, I think $X is a reasonable hourly rate for me" - with X being about 10-20% more than what you want to get, that way when the company negotiates you down (which is a very usual occurence), you can then counter with the rate you actually want and get it.
And then if they hear all that and tell you to pound sand or offer you something much smaller, that is when you consider looking for other employment and then the next discussion is you handing in your notice, because remember point 2 - the optimal time to negotiate a salary is when you are accepting a new job offer.
Good luck.