If a girl is born after Shkiah but before Tzeis, when is considered her birth date?

Both days L’chumra.

However, you should ascertain the exact time of birth so that there be no doubts. When most of the head emerges, is the time of birth according to Halacha. Also, if it’s immediately after Shkiah, it might still be considered day. The Shkiah in many calendars usually refers to sea level sunset. Additionally, the Alter Rebbe mentions the fact that Shkiah Ha’amitis is a few minutes later.

 

Sources:

מפי השמועה – ראה התקשרות גל׳ תשעא.

ולהעיר מדוגמתו – בנוגע לל׳ כסלו – היכל מנחם ב ע׳ לח ואילך. ובנוגע לאדר בשנה מעוברת – מפי השמועה בהתקשרות גל׳ תנג.

רוב פדחתו – שו״ע אדה״ז שלא, ה.

שקיעה האמתית – סדר הכנסת שבת.