Has anyone ever been denied unemployment for being termated for your job? Where I worked they terminated me from my teacher position, but offered me a lower paying job said it was more suitable to my education. I had been in this position for 25years, because I didn't finish my associated degree, they terminated me, When filed unemployment it was denied because they said they had offered me employment. Any help would be appreciated.

I was on unemployment recently, and found that out as well. They will not give you anything if they know you turned down a job offer. I wish it was as simple as "you pay into the system and get back money when you're unemployed", but sadly, they're very picky.
Maybe try asking for that lower position while you search for something else? If your salary is greatly decreased, sometimes unemployment will give you some benefits because of the sudden decrease. I had a friend that did that when she was working in retail..

Your claim wasn't denied because you were offered another position, you were denied because you were terminated. Unemployment is for layoffs only, although you can apply to collect if the Unemployment Office deems the firing was not legitimate. Teaching (a taxpayer paid job) is going through many changes and all teachers should have seen the warnings.

If you can find a pattern that shows selective firing, wherein other teachers with the same education, performance rating, and time worked were kept on at your old pay when you weren't, then you might have a case. Talk to your teacher's union.

You receive unemployment only till you find another job,
Some of the many rules are you have to be available to work and accept any suitable work within a certain dollar range

So yes, if you were offered work and refused it, that may be a reason to deny unemployment