First, we must understand Jins Sikah, a jins whose tonic is the so-called "quarter-tone" note, the third note of Jins/Maqam Rast. It occurs as the primary/root jins of Maqam Huzam, Maqam Sikah, and members of that family. It also occurs as a secondary jins tonicizing the third scale degree of Maqam Rast. The first example, here, shows Sikah as a root jins, in the Muwashshah "Jadaka-l-Ghaithu" (#01, 03, and #07):
Here is jins Sikah tonicizing the 3rd scale degree of Jins Rast, in "Ghannili Shwayya" (#10 & #14, with a variant of Sikah in #11). Notice, in these and the previous examples, that Sikah has a narrow span--only three notes, other ajnas (predominantly Hijaz and Bayati) using its third scale degree as a common tone/point of modulation.
Jins Pseudo-Sikah, then, is a jins that behaves similar to Sikah melodically, but is different intervallically (Sikah's intervals are a 3/4 step between 1 & 2 and a whole step between 2 & 3; Pseudo-sikah's intervals are a half-step between 1 & 2 and a whole step between 2 & 3). Rather than tonicizing the third scale degree of Rast, it tonicizes the third scale degree of Ajam or Hijaz; it is as though the Sikah has had its tonic moved up a quarter-tone in pitch. The casual observer might confuse this jins with Jins Kurd--to which Pseudo-Sikah is intervallically similar (1/2 step - whole step) or even Jins Saba Zamzama (Kurd with a lowered 4th, whose intervals are (1/2 step - whole step - 1/2 step). One has to ignore both the prominent raised "leading tone" underneath the Pseudo-Sikah tonic, as well as the melodic countour, the overall feel of the tonicization, and the types of acceptable modulations--all of which strongly resemble or are identical to Sikah--in order to make that mistake.
All of those features are on display in these examples, the first of which tonicizes the third scale degree of Ajam, within Maqam Zanjaran (hence the 6th scale degree above the root hijaz tonic), from the Mawwal Zanjaran "Amana Ya Leil" (#05 & #25). Note the strong relationship--also identical to Sikah--with Jins Hijaz on the third scale degree above the Pseudo-Sikah:
Here, Pseudo-Sikah tonicizes the third degree of Jins Hijaz, in this case where Hijaz is already a secondary Jins in Maqam Bayati Shuri. While there is no parallel usage for Sikah itself, the melodic consistency with the previous examples demonstrates that this is in fact the same Jins. Some might argue that it is not worth categorizing this as a jins at all--it is simply a momentary passing tonicization of the third scale degree of Ajam or Hijaz--but from my view, any consistent area of melody and tonicization is a jins, no matter how short in duration. From the Muwashshah "Hibbi Da3ani lil-Wisaal" (#03):