Where does “sentence-final particle” come from?

sentence-final particle (English) comes from English sentence, from Middle French sentence, from Old French sentence, from Latin sententia, from Latin sentīre, from Proto-Indo-European sent-, from Proto-Indo-European h₁es- — to be.

sentence-final particle (English): a word class that occurs at the end of a sentence or utterance that does not carry relational meaning, but may indicate linguistic modality, register or pragmatics

Definitions

a word class that occurs at the end of a sentence or utterance that does not carry relational meaning, but may indicate linguistic modality, register or pragmatics

Ancestry of “sentence-final particle”, step by step

sentence-final particle traces back through 3 separate lines of ancestry.

via English sentence

Step	Language	Word	Meaning
1	English	sentence	The decision or judgement of a jury or court; a...
2	Middle French	sentence	sentence judgement; verdict
3	Old French	sentence	—
4	Latin	sententia	opinion, thought, feeling; purpose,...
5	Latin	sentīre	—
6	Proto-Indo-European	sent-	to head for, to go, to travel; to feel
7	Proto-Indo-European	h₁es-	to be

via English final

Step	Language	Word	Meaning
1	English	final	A final examination; a test or examination given...
2	Middle English	final	—
3	Old French	final	final, definitive, last
4	Latin	fīnālis	Of or pertaining to boundaries
5	Latin	-ālis	—
6	Proto-Italic	-ālis	forms relational adjectives

via English particle

Step	Language	Word	Meaning
1	English	particle	A very small piece of matter, a fragment;...
2	Middle French	particule	—
3	Latin	particula	small part, particle
4	Latin	pars	part, side, piece, share; some; faction
5	Proto-Indo-European	per-	before, in front; first; to go through
6	Proto-Indo-European	pr̥tós	passed , crossed

Every word from Proto-Indo-European h₁es- →Every word from Proto-Indo-European sent- →Every word from Latin sentīre →