'vigilantly' is a correct and usable word in written English.
You can use it when you want to emphasize being on guard or alert about something. Example sentence: The bodyguards were vigilant in their duties, ready to protect the VIP at a moment's notice.
The border between theft and borrowing is also vigilantly patrolled by scholars.
A couple of senators are accused of accepting cut-price loans from a lender they should have been regulating more vigilantly.
Shiny new armoured personnel carriers, complete with turret-mounted machineguns, rumble vigilantly around potential trouble-spots.Against such firepower, the unarmed opposition would seem to stand little chance.
Why should we impose our values on others?Well, some values, such as gender equality and individual autonomy, are worth vigilantly defending, if not exactly imposing.
In the age of Hitler, Stalin, and Mussolini, it was profoundly wise to vigilantly stand guard against any possible slide into collectivist totalitarianism.
Locked in a zero-sum game (when one country wins, the other loses), the two superpowers watched each other vigilantly, eager for gains but also wary of the threat of nuclear war.
Of course, the IMF needs to be watched vigilantly.
IT staff watched vigilantly over us in our final hours, ensuring nobody attempted to make off with important files or equipment.
The site keeps the list of its most active pages updated itself, in part so it knows which pages need to be vigilantly watched, but they have been assembled into a useful graph by designer Ramiro Gómez.
"Titi would vigilantly chase me away from the door all day long," Sotomayor wrote, adding that it dawned on her only later that they were hiding from the police.
The mosquitoes kept tabs on us vigilantly everywhere we moved, indoors as well as out.
