Especially and specially are adverbs.
Especially means more than usual, most of all, in particular.
Judith likes chocolate, especially the dark one.
I like tea, especially the green tea.
He’s usually tired in the evening, but he was especially tired this evening.
Specially is used to talk about particular purpose or way of something.
This dress was specially tailored for Jane.
They ordered boots specially for her.
The pigs are specially trained to locate the truffles.