fristgerecht
by the deadline
Describes that something is completed within a set deadline or by a specific date.
Die Unterlagen müssen fristgerecht bis zum 31. Mai eingereicht werden.
The documents must be submitted by the deadline, by May 31.

on time / by the deadline
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by the deadline
Describes that something is completed within a set deadline or by a specific date.
Die Unterlagen müssen fristgerecht bis zum 31. Mai eingereicht werden.
The documents must be submitted by the deadline, by May 31.

The word is made up of 'die Frist' (the deadline) and 'gerecht' (appropriate, correct). Something is 'fristgerecht' (by the deadline) when it is completed in accordance with the deadline, that is, on time.
Eine fristgerechte Kündigung muss bis zum dritten Werktag des Monats erfolgen.
A timely termination must be made by the third working day of the month.
'Fristgerecht' (by the deadline / on time) is very often used as an adverb to describe a verb. It answers the question 'How was something completed?'.
Der Bericht wurde fristgerecht fertiggestellt.
The report was completed by the deadline.
This word belongs to formal language, especially administrative and business language. It is used with contracts, invoices, applications, and official submissions.
Die Bewerbung muss fristgerecht bei der Personalabteilung eingehen.
The application must be received by the HR department by the deadline.
Typical verbs combined with 'fristgerecht' (by the deadline) are actions with a deadline: 'einreichen' (to submit), 'abgeben' (to hand in), 'bezahlen' (to pay), 'liefern' (to deliver), or 'erledigen' (to complete).
Wenn Sie die Ware nicht fristgerecht liefern, müssen wir vom Vertrag zurücktreten.
If you do not deliver the goods by the deadline, we will have to withdraw from the contract.
at the latest
'spätestens' and 'fristgerecht' can both have to do with a deadline. 'spätestens' names the latest point by which something has to happen. 'fristgerecht' describes the result: something was completed within the deadline. 'spätestens' often appears with a specific time or date. 'fristgerecht' sounds somewhat more formal and fits well with applications, payments, cancellations, or submissions. In short: 'spätestens' says by when; 'fristgerecht' says that the deadline was met.

Ich reiche die Anmeldung für die Veranstaltung fristgerecht ein.
I submit the registration for the event by the deadline.
Schickt mir den Bericht bitte spätestens nach der Arbeit.
Please send me the report by after work at the latest.