There still must be some descendants of the Spartan colonists in surrounding villages and general area, it probably wouldn't have disappeared entirely, but I get what your saying that events in history may change demographics, but at the same time some original must be there as well.
Taranto would fall under the county of Apulia which comprises of many more towns and villages. According to Eupidia these are the main HG's.
[TABLE="class: fixed, width: 970"]
[TR]
[TD="class: I1, align: center"][/TD]
[TD="class: I2b, align: center"][/TD]
[TD="class: I2b, align: center"][/TD]
[TD="class: I2, align: center"][/TD]
[TD="class: R1a, align: center"][/TD]
[TD="class: R1b, align: center"][/TD]
[TD="class: G2a, align: center"][/TD]
[TD="class: J2, align: center"][/TD]
[TD="class: J1, align: center"][/TD]
[TD="class: E1b, align: center"][/TD]
[TD="class: T, align: center"][/TD]
[TD="class: L, align: center"][/TD]
[TD="class: Q, align: center"][/TD]
[/TR]
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[TABLE="class: fixed, width: 970"]
[TR]
[/TR]
[TR]
[TD="class: left"]Apulia[/TD]
[TD="class: I1, align: center"](10)[/TD]
[TD="class: I2b, align: center"](4)[/TD]
[TD="class: I2b, align: center"](1)[/TD]
[TD="class: I2, align: center"](15)[/TD]
[TD="class: R1a, align: center"]13[/TD]
[TD="class: R1b, align: center"]117[/TD]
[TD="class: G2a, align: center"]52[/TD]
[TD="class: J2, align: center"]94[/TD]
[TD="class: J1, align: center"]13[/TD]
[TD="class: E1b, align: center"]82[/TD]
[TD="class: T, align: center"]6[/TD]
[TD="class: L, align: center"]1[/TD]
[TD="class: Q, align: center"]0[/TD]
[TD="class: other, align: center"]426[/TD]
[/TR]
[TR]
[TD="class: left, width: 180"][/TD]
[TD="class: I1, align: center"]I1 2.5%[/TD]
[TD="class: I2b, align: center"]I 2b1 1%[/TD]
[TD="class: I2b, align: center"]0%[/TD]
[TD="class: I2, align: center"]I2a 3.5%[/TD]
[TD="class: R1a, align: center"]R1a 3%[/TD]
[TD="class: R1b, align: center"]R1b 27.5%[/TD]
[TD="class: G2a, align: center"]G 12%[/TD]
[TD="class: J2, align: center"]J2 22%[/TD]
[TD="class: J1, align: center"]J*+J1 3%[/TD]
[TD="class: E1b, align: center"]E1b1b 19%[/TD]
[TD="class: T, align: center"] T 1.5%[/TD]
[TD="class: L, align: center"]0%[/TD]
[TD="class: Q, align: center"]0%[/TD]
[/TR]
[/TABLE]