One of the major difficulties that arises when selecting aptamers containing a G-quadruplex is the correct amplification of the ssDNA sequence. Can aptamers containing a G-quadruplex be selected from a degenerate library using non-equilibrium capillary electrophoresis (CE) of equilibrium mixtures (NECEEM) along with high-throughput Illumina sequencing? In this article, we present some mismatches of the G-quadruplex T29 aptamer specific to thrombin, which was PCR amplified and sequenced by Illumina sequencing. Then, we show the proportionality between the number of sequenced molecules of T29 added to the library and the number of sequences obtained in Illumina sequencing, and we find that T29 sequences from this aptamer can be detected in a random library of ssDNA after the sample is fractionated by NECEEM, amplified by PCR, and sequenced. Treatment of the data by the counting of double-stranded DNA T29 sequences containing a maximum of two mismatches reveals a good correlation with the enrichment factor (fE). This factor is the ratio of the number of aptamer sequences found in the collected complex sample divided by the total number of sequencing reads (aptamer and non-aptamer) plus the quantity of T29 molecules (spiked into a DNA library) injected into CE.