一. colon (:)  

   In most cases, you don’t need to capitalize after a colon.

  Rule 1. Capitalize the first word of a quote when the quote is a complete sentence.

  Examples:  Mario asked, “What is everyone doing this weekend?”

  Rule 2. Don’t capitalize the first word of partial quotes.

https://www.grammarly.com/blog/capitalization-after-colons/

二. semicolon(;)   use a lowercase letter after a semicolon

   Rule 1. Use a semicolon in place of a period to separate two sentences where the conjunction has been left out.

   Examples:  Call me tomorrow; I will give you my answer then.
They went to the scariest movie they could find; they didn’t invite their youngest sister.

   Rule 2. It is preferable to use a semicolon before introductory words such as namely, however, therefore, that is, i.e., for example, e.g., or for instance when they introduce a complete sentence. It is also preferable to use a comma after the introductory word.

   Examples:   You will want to bring many backpacking items; for example, sleeping bags, pans, and warm clothing will make the trip better.
As we discussed, you will bring two items; i.e., a sleeping bag and a tent are not optional.

   Rule 3. Use the semicolon to separate units of a series when one or more of the units contain commas.

   Example:   This conference has people who have come from Boise, Idaho; Los Angeles, California; and Nashville, Tennessee.

   http://data.grammarbook.com/blog/semicolons/semicolons/