american english - An 'h' or a 'h' when just saying the letter?

I know for words starting with the letter 'h' the usage of "A" vs. "An" depends on how its pronounced.

A - Before a word start­ing with a pro­nounced, breathy “h,” use “a.” Examples: A hotel; A happy time; A his­tor­i­cal day; A healthy, happy baby.

An - Use “an” with words begin­ning with an unpro­nounced “h.” Examples: An herb gar­den; an hour; an honor; An heir.

http://editingandwritingservices.com/a-or-an-before-words-beginning-with-h/

But what about when your word is just the character 'h' such as in the sentence:

This word starts with a/an 'h'

"An" seems to fit better when I say it, and I suppose it fits the definition of not starting with a breathy "h" sound. But also its not an unpronounced 'h' because that's literally all you're pronouncing.

Which is correct?

Answer

In some regions of England, the letter is called "haitch". In those dialects, the phrase will naturally be "a haitch".

Everywhere else, the letter is called "aitch". In those cases, the phrase will be "an aitch".

It doesn't matter in the slightest how it is spelt, or whether it might have a funny sort of representation of a sound that isn't quite /h/ in it: the rule about 'a' vs. 'an' is simly about whether the word starts with a vowel sound.