Is there a such word or concept as alphanumatics???

Not in the mainstream (to my knowledge), but anyone is free to coin a
new word for their purposes.

A Google search for "alphanumatics" produces no results. A search for
"alphanumatic" produces one site using the word:

"The large back lit LCD display provides high alphanumatic channel
designations up to 7 characters frequency, memory channel number,
mode, signal meter and transmit indicator."

Kenwood Electronics UK
http://www.kenwood-electronics.co.uk/html/products/comms/pdfs/pdf_tk80.pdf

From the context, I would say that this is almost certainly a typo for
"alphanumeric."

There is a company called Alpha Pneumatics, Inc:

Alpha Pneumatics
http://www.alphapneumatics.com/

I also found where the word was used in place of the correct word
"alphanumeric". I found this error on seven sites in all.

Regards;
tutuzdad-ga

If I coin a word or phrase that represent a concept, what is the best
way to protect my rights for that word or phrase, is it copyright or
trademark?

In the United States, a word cannot be copyrighted. You need to
investigate registering a trademark.