While pp. 183-187 of World Braille Usage does not list capital or upper case letters, they do exist. An online search of Greek capital letters confirms this, along with the information that capital letters are seldom used. p. 49 of the UEB Rules lists in section 4.5 the capital Greek alpha. This listing would be used for individual Greek letters used in English contexts or English technical materials.
From a previous query, I'm assuming you are using WBU, which does not list information about punctuation. So, for the capital letter in your sample, use the UEB prefix dot 6 as outlined in UEB section 8 along with dot 1 for alpha. If we need to discuss the print mark before your capital letter, please send along a print sample.
The print sample shows that you need information on p. 187 of <i>World Braille Usage. </i>What looks like an apostrophe before the A in the Grrek word you are asking about could either be an elision or a breathing mark. There's no indication that is an elision. Elision is defined as "the omission of one or more sounds (such as a vowel, consonant, or a whole syllable) in a word or phrase.
That apostrophe is actually a breathing mark. You have both the spiritus asper (rough breathing dots 125) and the spiritus lenis (smooth breathing mark dots 356) in your print sample. They are mirror images of each other in print, placed above some of the lower case Greek letters in your sample. You'll also see them above the letter, prior to the accent, in some of the Greek words also.
I am unable to Braille this for you because of my current location, but WBU gives you the information you need. (WBU is found on the Perkins.org site). The breathing marks precede the accent signs.