<p>Is it correct to write conjunction after semicolon?
e.g. Alice was not just a great speaker;but also a great president</p>
<p>In the sentence you have, a semicolon would not be proper. The semicolon is used to connect the independent portions of a compound sentence when you don’t put in a coordinate conjunction (such as “and” or “but”). However, it can be used before a coordinate conjunction to prevent confusion when the lead independent phrase has its own comma phrases; example: "Alice was a great speaker, a great president, and a convincing person; but she failed to convince the committee to fund her cause.</p>
<p>Your example doesn’t need any punctuation!</p>