Company Y doesn't know that my current position is an apprenticeship since I've put it in "work history" from 201X until now in my resume.
Well, then you lied to them. Work history is supposed to be starting after your education, and "Ausbildung" is your education. They will probably see you in a very different light when you tell them your "work history" is actually the first two years of an apprenticeship.
If I want to accept the new position I would have to quit my current job and therefore cancel my apprenticeship in which the finals start in four months and would leave me without any sort of diploma that I finished my apprenticeship.
That's correct. And let me add this personal opinion: cancelling your education just four months before you can finish it and start your life without any "Berufsabschluss" (certification/diploma) is extremely stupid. You will need a "Berufsabschluss" for your next 70 years. Not finishing your education is going to harm you for the rest of your life. If you don't plan on dying early in 2017 or winning a few million the lottery, this is stupid, stupid, stupid.
I do not know if it is possible to finish the apprenticeship at company Y.
It is, but you need a lot of work from both your old and new company and both will not want to invest this amount of work in you, especially not the company you intend to leave.
Should I tell them on the phone interview about my apprenticeship?
Yes. By all means yes. Lying on an interview is a bad decision. If you lied on your interview, the company can fire you on the spot at any time they see fit. So if you lie and you start to work there and they want to get rid of you after 4 years, they can just say "you lied all that time ago on your interview, you are fired, bye bye, no severance package". And since you were fired for cause, you would not even get unemployment benefits. Do not lie on the interview. Ever.
Is it unethical to my current employer to leave right now?
Yes. Because your apprenticeship is a deal between you and your employer. Your employer is paying you. Not a full paycheck, but maybe a third of what you would earn if you had finished your education. That is because he has to spent time and effort to educate you for three years and you are barely productive in at least the first year. In the third year you are supposed to be as productive as a new junior role. So while your employers pays you, you deliver no value but only costs in the first year, maybe break even in the second and due to your low income actually deliver value on the third year. So overall, losing money in the first year, breaking even and then making money in the third year, your employer is supposed to do ok.
Now if you take the education, where your employer even pays you to get educated and then when it's payback time you just vanish and say bye bye, that's unethical. You have a contract signed for three years. Breaking that contract is unethical.
What is an acceptable manner to approach this?
Don't. Just don't. You are ruining your future. You are dropping your education, you are not getting a good reference from the only person you have ever worked for and for what? 4 months of a higher paycheck?
Finish your education. It's perfectly fine to look for other jobs afterwards. Compare your current employers offer to other offers. And you can certainly start looking now and if you find something, take an offer with a starting date after your education's end. But only after you have finished your education and after you have fulfilled your contract should you switch your job. Anything else is career suicide.