'gwyddost ti' comes from the short-form (conjugated) present tense of gwybod.
Its question form (wyddost ti?) is used in very shortened form ('sti, 'sdi) as a tag question - you know? - in some parts of Wales (definitely in the north-west). Other variants are also common, such as wsti?, ch'mod? (from dych chi'n gwybod?) and t'mod? (from wyt ti'n gwybod?).
[gwybod is one of very few verbs to have a true conjugated present tense separate from its future tense in Modern Welsh. As far as I know, the only others are bod (very common) and adnabod (very unusual to see it these days). You will not usually hear it in colloquial Welsh except in set phrases such as:
- Pwy a ŵyr? - Who knows?
- Wyddoch chi beth...? - Do you know what...?