“να σου δώσω” means “to give something to you”.
“να σε δώσω” means “to give you away”.
However, in northern Greece (Thessaloniki area) they also use the later form “να σε δώσω” to say “to give something to you”. This is definitely not a correct form, it is an idiom and used only in oral speech.
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Vasiliki Baskou, Instructor/Director, https://learn-greek-online.com.