The invention relates to a modified copolyester slice or fiber and a relative preparation, wherein the slice is copolymerized from terephthalic acid, ethandiol, isophthalate esters of sulfonic acid sodium (or potassium), and fatty group dibasic alcohol (or relative alkylate) with side chain. And the preparation comprises that (1), mixing the ethandiol and the fatty group dibasic alcohol (or relative alkylate) into a mixed alcohol, adding catalyzer and stabilizer to esterify the terephthalic acid under 220-260Deg. C, (2), adding 1-9%mol isophthalate esters of sulfonic acid sodium (or potassium) relative to the terephthalic acid for polycondensation at 250-300Deg. C, (3), drying, fusing, spinning, and drawing to obtain the modified copolyester filament. The inventive product can dye anion paint and disperse paint into deep color at normal pressure, with better feeling, high contraction, hidden micro coiled property, simple preparation, low cost and batch production support.