Due to the extreme extinction towards the Galactic centre ($A_{V} sim 30$ mag), its stellar population is mainly studied in the near-infrared (NIR) regime. Therefore, a proper analysis of the NIR extinction curve is necessary to fully characterise the stellar structure and population of the inner part of the galaxy. We studied the dependence of the extinction index ($alpha_lambda$) in the NIR on the line of sight, wavelength, and extinction. We used the GALACTICNUCLEUS imaging survey, a high angular resolution catalogue ($0.2$) for the inner part of the Galaxy in $JHK_s$, and studied the spatial variation in the extinction index. We also applied two independent methods based on red clump stars to compute the extinction index between different bands and its variation with wavelength. We did not detect any significant line-of-sight or extinction variation in $alpha$ within the studied region in the nuclear stellar disc. The extinction index between $JH$ and $HK_s$ differs by $0.19 pm 0.05$. We obtained mean values for the extinction indices $alpha_{JH} = 2.43pm0.03$ and $alpha_{HK_s} = 2.23pm0.03$. The dependence of the extinction index on the wavelength could explain the differences obtained for $alpha_lambda$ in the literature since it was assumed constant for the NIR regime.
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