"inst." is an abbreviation for "instant", which means the current month or year, depending upon its context. For example, "the 3rd day of March, inst.," means March 3 of the current year. "The 3rd day, inst.," means the 3rd day of the current month.

In Civil War correspondence you may also see the abbreviation "ult.", an abbreviation for "ultimo," which means the previous month or year, depending upon its context.

You may also see the phrase "12 m.", an abbreviation for "12 meridian", which means 12 noon.

These were widely used in the Civil War, but have since gone out of fashion and are rarely, if ever, seen these days.