It doesn't as shown in the tips here https://www.duolingo.com/skill/el/Basics-1/tips-and-notes. Prepositions are followed by the accusative (rule of thumb), correct.
You may see/hear it as μιαν in the accusative, most likely from older speakers, but that's it. (Most likely before a vowel I would expect, e.g. μιαν ημέρα.)
Κοντά on its own means "nearby". Το σπίτι μου είναι κοντά=My house is nearby. If you want to say "near (to)" something, you have to use κοντά + Indirect object. The indirect object uses either the weak genitive pronoun forms (μου,σου,του etc), or σε+strong accusative pronoun form or σε+noun. So, είμαι κοντά σου/σε εσένα=I am near you, το σπίτι μου είναι κοντά σε ένα πάρκο=my house is near a park, το σπίτι μου είναι κοντά στο πάρκο (στο=σε+το)= my house is near the park, το σπίτι μου είναι κοντά στο δικό σου=my house is near yours. Hope these help!