I´m searching for a list of exponents like ¹²³ and so on and the same with letters. Note these still remain superscripted even in plain text. Does something like these exist? If not, how can I create those?

(I need them for a website-project)

Unicode versions of superscripted/subscripted characters exist for all ten digits but not for all letters. They remain superscripted/subscripted in a plain-text environment without the need of format tags such as <sup>/<sub>.

However (as of v14), not all letters have Unicode superscripts. Furthermore, they are scattered along different Unicode ranges, and are in fact used mainly for phonetic transcription. Additionally, they are used for compatibility purposes especially if the text does not support markup superscripts and subscripts.

Exponent characters:

These are mostly used for mathematical and referencing usage.

 - ⁰ [U+2070]
 - ¹ [U+00B9, Latin-1 Supplement]
 - ² [U+00B2, Latin-1 Supplement]
 - ³ [U+00B3, Latin-1 Supplement]
 - ⁴ [U+2074]
 - ⁵ [U+2075]
 - ⁶ [U+2076]
 - ⁷ [U+2077]
 - ⁸ [U+2078]
 - ⁹ [U+2079]
 - ⁺ [U+207A]
 - ⁻ [U+207B]
 - ⁼ [U+207C]
 - ⁽ [U+207D]
 - ⁾ [U+207E]
 - ⁿ [U+207F]
 - ⁱ [U+2071]

The "linear", "squared", and "cubed" subscripts are the most familiar and are found in Latin-1 Supplement. All the others are found in Superscripts and Subscripts. Add 0x2070 to all the non-Latin-1 Supplement superscripts to obtain the code point value of these digits. See this Wikipedia article and the official Unicode codepage segment.

Interesting notes

There are also subtle differences between <sup> subscripts and Unicode subscripts; Unicode subscripts are entirely different codepoints altogether, and some fonts professionally design subscripted letters because <sup> subscripts may look thin.

Compare x² with x², similarly x⁺ with x⁺ (the first involves Unicode, the second is markup)

The best solution is to use markup, such as <sup>.