The semicolon should always be put outside quotation marks unless it forms a part of the quotation itself.
“Take care of the cents and the dollars will take care of themselves”; a very wise old saying.
THE COLON
The colon marks the place of transition in a long sentence consisting of many members and involving a logical turn of the thought. Both the colon and semicolon are much less used now than formerly. The present tendency is toward short, simple, clear sentences, with consequent little punctuation, and that of the open style. Such sentences need little or no aid to tell their story.
Rules for the Use of the Colon
1. Before as, viz., that is, namely, etc., when these words introduce a series of particular terms in apposition with a general term.
The American flag has three colors: namely, red, white, and blue.
2. Between two members of a sentence when one or both are made up of two or more clauses divided by semicolons.