Actually, there are two more ㅣ preceding vowels ㅒㅖ, but these are rarely used.

All the 8 vowels make ㄷand ㅌ pronunciation changing to ㅈ and ㅊ.

Here are examples of changing.(ㅣ,ㅑ, ㅕ, ㅛ, ㅠ, ㅣ, ㅒ, ㅖ )

굳이→구디→[구지],

해돋이→해도디→[해도지],

같이→가티→[가치],

닫혀→다텨→[다쳐],

붙이다→부티다→[부치다],

굳히다→구티다→[구치다]

 Here are examples of not changing.

같은→가튼

곁을→겨틀

곁에→겨테

밑에서→미테서

First of all thank you Heesob Park for your comment, but let me be more specific.

같이 [가치]  as you can see here ㅌpronounce as ㅊ sound because it followed by the vowel ㅣ.

So, what I want to know is all the vowels that make ㄷand ㅌ pronunciation changing to ㅈ and ㅊ.