"Especially" is used to emphasize something or indicate a high degree, while "specially" refers to something done for a specific purpose or unique situation. ^{britannica.com 4 1 2 3 5}

Examples:

• "I especially love the way this dress fits." (Emphasizing liking) ^{grammargiant.com 1}
• "The restaurant is known for its seafood, especially its lobster dishes." (Emphasizing standout items) ^{grammargiant.com 1}
• "I made these cookies specially for you." (For a specific purpose) ^{grammargiant.com 1}
• "The company developed a new product line specially for the holiday season." (Unique purpose) ^{grammargiant.com 1}
• "The dance was choreographed specially for the differently abled." (Unique purpose) ^{byjus.com 3}
• "He became visibly upset, especially when they called him an outcast." (Emphasizing emotional reaction) ^{byjus.com 3}