What does the a mean in the following sentences?
She is a do it like this.
Sam is a visit the new market today.
Does the word a represent a future action like :
Sam will visit the new market today. ?
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What I assume you to be referring to here, is the English "a" preposition. Though the way that you have written it in your OP is not in any recognisable syntax. It is not "slang", but an older form of the language.
It has largely fallen into disuse, except in some regional dialects in Britain. (My own family in Norfolk, when I was a child in the 40s, 50s, and early 60s used it extensively, especially my grandparents.)
It not only applies to verbs but to nouns too. There are a multiplicity of forms. All references are to the OED.
Category I refers to nouns:
"Expressing position within" - 1974 W. Leeds Herefordshire Speech 45 See you a church. i.e. "See you in church". (OED sense 1)
"In expressions of time" - 1996 S. Moylan Lang. Kilkenny 14 He was here a Sunday. (sense 3a)
"Expressing place or position in relation to something else" 1987
F. Graham New Geordie Dict. 5 A this side—on this side.(sense 7)
"Expressing partition into" - 1888 F. T. Elworthy W. Somerset Word-bk. (at cited word), They be all a pieces. (sense 9)
Category II. With a verbal noun or gerund, forming part of a verbal expression. (Now usually written with a hyphen or as one word with the verbal noun.)
"11. Expressing action, with a verbal noun or gerund taken actively. Now arch. and regional. a. After be (or occasionally another verb expressing state) and before a verbal noun: engaged in"
1895 T. Hardy Jude i. ii. 9 Just now he's a-scaring of birds for Farmer Troutham.
1928 A. E. Pease Dict. Dial. N. Riding Yorks. 1/1 He was a-gannin' ower t'mooer.
1960 in Dict. Amer. Regional English (1985) I. 2/1 That's the only way you knowed where you was a-goin'.
2003 Daily Tel. 18 Nov. 23/1 The invitation has been such a long time a-coming. (sense 11a)
"b. After a verb denoting or implying motion and before a verbal noun: to, into"
c1960 Wilson Coll. in Dict. Amer. Regional English (1985) I. 1/2 Pappy went a-visiting yesterday.
1972 Islander (Victoria, Brit. Columbia) 2 Apr. 4/3 In England, the children until the recent past—and even, in some parts of the country today—still go a-shriving.
2005 Daily Tel. 20 June 9/1 Eligible bachelors..meet marriageable ladies..at a country pub to go a-courting in the Cotswolds. (sense 11b)