早晨(zǎo chén) - early morning, daybreak in Mandarin

早晨 is the early part of the morning, roughly from first light to about nine. It is slightly more written and more northern than 早上, which covers the same ground in ordinary speech across the whole country.

Use it as a time word, which in Mandarin means it goes before the verb, not after: 我早晨去跑步 (I go running in the morning), never 我去跑步早晨. It also takes 在 optionally, so 在早晨 and bare 早晨 are both fine.

For a greeting, stick with 早上好 or just 早. 早晨好 exists but sounds stiff, and in Cantonese-influenced speech 早晨 on its own is itself the greeting, which is a nice thing to recognise but not something to import into your Mandarin.