According to the table, the most clever is correct according to the rules. There are however some exceptions to these rules including narrow/narrowest and simple/simplest. Both are acceptable when the adjective has two syllables and the stress is on the first part of the word. You can’t have two options when the word has three or more syllables
Learn more about Superlative adjectives in my guide here and find a full list of superlative adjectives here.
The cleverest can sound a little strange to your ear because of the -er at the end of clever. Many people add -er to every comparative adjective when they are learning English(children and non-native speakers).Comparative adjectives compare two things.
Cleverer or more clever?
Cleverer and more clever are both acceptable. These are examples of comparative adjectives.