What does "I'za" mean?

Solution 1:

It's a form of

I'se

var. I's, Ise...

• (N. UK reg. or arch.) I shall.
  I'se warrant him nane of your whingeing King George folk. (Walter Scott, Waverley, Vol. II)

• (N. UK, S. US reg., AAVE) I am, via reg. dial. 'I is'.
  Ise, I am or I will. (Wm. Carr, Dialect of Craven... York)
  I'se tinking wha' jolly time we will hab on Saturday arternoon, down under ole elm trees, on bank ob de riber. (W.L.G. Smith, Life at South)

that picked up the indefinite article a because of the rhythm of the sentence. Eye dialect is often used mockingly; the example here seems to be self-mocking in the interest of gaining more authority for the modest claim of 'some knowledge' of computers.

Solution 2:

It's simply a way of contracting "I is a". In your context I would guess it's a faked patois.

Solution 3:

"He sez I'za gonna look like you some day" . google books

and

I'se

1847 in representations of African-American vernacular, a contraction of I is (see is), irregular for I am. (etymonline)

Variations in AAVE an other colloquial AmE: I is, I am Similar to fidna: a fixin to. Seen more written than spoken though I did hear, in jest: I'za gonna whup yo arse.

Solution 4:

I have never come across it before. As it will only occur in extremely informal spoken English, you are unlikely to find it in any grammar or dictionary, but it could be used in literature to try and convey a particular way of speaking.

From the sentence I would agree with your reading of it being a contraction of I is a; the /s/ would be voiced, so in the contraction it is represented by a z, and the duplicate /i/ is elided.