There is no such word as specially. There a word, special. And there is a word, especially.

As for formal usage "especially" has a more limited use than "specially". Specially is always used in preference to especially when the sense is one of being out of the ordinary: He has been specially trained. Specially is also used when something is referred to as being for a particular purpose: The word was specially underlined for you. Where an idea of pre-eminence or individuality is involved, either especially or specially may be used: He is especially (or specially) good at his job. In informal English, however, specially is usually preferred in all contexts and both 'specially' and 'especially' are less distinguishable.