Deep near-infrared photometric surveys are efficient in identifying high-redshift galaxies, however they can be prone to systematic errors in photometric redshift. This is particularly salient when there is limited sampling of key spectral features of a galaxy's spectral energy distribution (SED), such as for quiescent galaxies where the expected age-sensitive Balmer/4000 A break enter the \(K\)-band at \(z>4\). With single filter sampling of this spectral feature, degeneracies between SED models and redshift emerge. A potential solution to this comes from splitting the \(K\)-band into multiple filters. We use simulations to show an optimal solution is to add two medium-band filters, \(K_\mathrm{blue}\) (\(\lambda_\mathrm{cen}\)=2.06 \(\mu\)m, \(\Delta\lambda\)=0.25 \(\mu\)m) and \(K_\mathrm{red}\) (\(\lambda_\mathrm{cen}\)=2.31 \(\mu\)m, \(\Delta\lambda\)=0.27 \(\mu\)m), that are complementary to the existing \(K_\mathrm{s}\) filter. We test the impact of the \(K\)-band filters with simulated catalogues comprised of galaxies with varying ages and signal-to-noise. The results suggest that the \(K\)-band filters do improve photometric redshift constraints on \(z>4\) quiescent galaxies, increasing precision and reducing outliers by up to 90\(\%\). We find that the impact from the \(K\)-band filters depends on the signal-to-noise, the redshift and the SED of the galaxy. The filters we designed were built and used to conduct a pilot of the FLAMINGOS-2 Extra-galactic Near-Infrared \(K\)-band Split (FENIKS) survey. While no new \(z>4\) quiescent galaxies are identified in the limited area pilot, the \(K_\mathrm{blue}\) and \(K_\mathrm{red}\) filters indicate strong Balmer/4000 A breaks in existing candidates. Additionally we identify galaxies with strong nebular emission lines, for which the \(K\)-band filters increase photometric redshift precision and in some cases indicate extreme star-formation.