Especially and specially can often both be used with the same meaning. However, here are some points that you can note about it:
1. ‘especially’ is often used to mean ‘above all.’
Example: I like all kinds of sweets, especially gulabjamun.
2. ‘especially’ follows a subject.
Example: We all like music. My mother, especially, is very enthusiastic about
buying new records and going to shows.
3. ‘especially’ is preferred before prepositions and conjunctions.
Example: I drink a lot of coffee, especially when I’m working. / We love to go
swimming, especially in summer.
4. ‘specially’ is used with a past participle, to mean ‘a particular purpose.’
Example: Those cookies were specially made for me.
5. ‘special’ is normally used as adjective.
Example: He took special trouble over his work.