Is there such thing as an "Alpha" Betta fish?

No, but all male bettas think they are alpha males. That's why they fight with only each other.

BTW, betta is pronounced bet-tah, not bay-tah. Two t's make a short "e."

Bay-tah is spelled beta and is the second letter of the Greek alphabet. The first letter is "alpha."

Also, there is a grocery store chain called Alpha-Beta in California.

Yes, but generally it refers to a female betta. Females in a single tank with generally fight for a week until they establish a pecking order. Then they will generally get along unless you remove or add one.

In some cases a breeder will have a large tank with 1-3 males, and a bunch of females. In this case the alpha will likely be a male. Note in this case the breeder has raised the betta together from birth, and removed all, but the most mild mannered of males, and the more aggressive females. The odds of a random male betta getting along with a group of females is really low.

That's cute. I recently purchased an Omega betta. (no just kidding). I would imagine in their natural environment bettas do have a pecking order when living together. A male over sees the rearing of the young, so he probably does become the Alpha of his fry.

Take Care

When female bettas are kept together (which they can be, usually) there is one Alpha female. If this female is removed from the group, the others will quickly begin fighting and attacking each other to try to become the new Alpha.

Yep, it's usually the father of a bunch of related bettas.

Probably, Leader of the Pack.

I have a Mas-ta Betta...

He's purple, large, anti-social, lonely, and his tank is always filled with fluid. *ponders*

I had one of those.

The other fish came to resent his domineering attitude, and one morning I found him floating Upsilon.

haha there HAS to be!