Special?

Interesting discussion when I showed my post to 2020 blog to two colleagues and they both said me: "Specially? It's especially. I'm sure". I was really surprised and searched the internet and Cambridge dictionary.

especially adverb (ALSO specially)
very much; particularly; for a particular reason

specially adverb (ALSO especially)
for a particular purpose

Not clear? Try this:

Special is a common adjective. Specially is its adverb form. Special means "particular, distinguished in a distinct way, or designed for a particular purpose." Specially means "particularly, in a disintguishing manner, or for a particular purpose."
Especial is an uncommon adjective. Especially, its adverb form, is much more common. Especial means "exceptional, noteworthy, or particular." Especially means "exceptionally, in a noteworthy manner, or particularly."

So, I wrote especially, but it's still unclear for me... :S