Aylostera pseudominuscula was originally described, as Echinopsis pseudominuscula, by C. Spegazzini in Anales Museum Nacional Buenos Aires ser. 3, 4: 488, in 1905.

Here is the text of the description in Latin as published, but you should look up the original for more details. The English translation below is my own.

Echinopsis ? pseudominuscula Speg. ( n. sp.)

Echinocactus pseudominusculus Speg. in litt. et adumbr.

Diag. Euthyacantha, pusilla, subcylindracea obscure viridis nitida, simplex v. basi prolifera; costis 13 in tuberculis hemisphaerico-subtetragonis solutis ; areolis ellipsoideis; aculeis omnibus setaceis subaequilongis parvis albescentibus, 7-14 radiantibus, 1-4-centralibus; floribus inodoris pleurogenis numerosis parvis eximie infundibuliformibus, extus viridibus, parcissime squamosis atque vix villosulis, tubo perigoniali elongato angusto cum stylo concreto, petalis atro-purpureis.

Hab. Rarissime in alpinis (3.500 m alt. s. m.) Prov. Salta.

Obs. Cormus parvus (50 mm alt. =35 mm diam.), superne applanatus centroque lenissime umbilicatus; costae obtusae e tuberculis (5 mm alt. = 7-8 mm diam. bas.) conflatae; areolae cinereo-velutinae, spatio 7-8 mm inter se separatae; aculei (3-5 mm long.) primo ochracei v. fusco-rosei, serius albi apice ferruginei, postremo albo-subhyalini. Flores pulchelli (25 mm long.) ovario globoso glabro bracteolis 7-8 ornato, tubo perianthico cilindrico (15 mm long.) cum stylo concreto e viridi roseo-purpurascente, paucissime squamoso; bracteolis perianthicis ad axillam albo-lanuginosis; petalis oblanceo-lato-spathulatis obtusis (15-18 mm long. = 5-7 mm lat.); staminum filamentis albis, antheris flavis, stylo roseo laciniis stigmaticis 6 albis coronato.

Species a generi desciscens tubo perianthico angusto et solido!, praecedenti notis plurimis conveniens sed certe distinctissima.

English translation

Section Euthyacantha, small, short-cylindrical, dark shiny green, single or clustering at the base; 13 ribs with weak hemispherical or tetragonal tubercles; areoles ellipsoidal; hair-like more or less equal small spines, whitish radiating 7-14, and 1-4-central; numerous small odorless flowers from the base of the ribs, externally green, slightly scaly and a little hairy, with a narrow elongated floral tube with a stiff style, petals atro-purpurea (dull red with a suggestion of blue).

Habitat: very rare, alpine (3.500 m alt. s. m.) Prov. Salta.

Small tap root (50 mm height, 35 mm in diameter), upper flat with the centre slightly constricted; ribs are blunted by the tubercles (5 mm height, 7-8 mm diameter at the base), conflating; areoles velvety-grey, 7-8 mm apart; spines (3.5 mm) at first ochreous to brownish-pink, later white with rusty tips, and finally white-colourless. Flowers pretty (25 mm long).

Ovary smooth spherical, dressed by 7-8 bracts, perianth tube cylindrical (15 mm), with a stiff reddish-purple and green style, very few scales; axils of the perianth bracts with white wool; petals oblanceolate, blunt-spatulate (15-18 mm long, 5-7 mm wide) stamen filaments white, yellow anthers, style with pink stigmas fringed with a crown of 6 white stigmatic lobes.

Species departs from the characteristics of the genus by having a narrow floral tube and strong perianth. Preceding the most appropriate remarks however certainly distinct.