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We study the connection between Ly α emitters (LAEs) and metal-enriched ionized gas traced by C IV absorption at redshift z ≈ 3-4 in 28 quasar fields with high-resolution spectroscopy from the MUSE Analysis of Gas Around Galaxies survey. In a sample of 220 C IV absorbers, we identify 143 LAEs connected to C IV gas within a line-of-sight separation $\pm 500\rm \, km\, s^{-1}$, equal to a detection rate of 36 ± 5 per cent once we account for multiple LAEs connected to the same absorber. The luminosity function of LAEs associated with absorbers has an ≈2.4 higher normalization than the field. The analysis of the LAE-C IV correlation function suggests that metal-enriched gas arises both in the haloes of the LAEs and from locations not connected to galaxies. C IV absorbers with higher equivalent width are more often associated with LAEs and C IV systems are twice less likely, especially at low equivalent width, to be found near LAEs than strong H I absorbers. The covering fraction in groups is up to ≈3 times larger than for isolated galaxies. Similar results are found using Si IV as tracer of ionized gas. We propose three components to model the gas environment of LAEs: (i) the circumgalactic medium of galaxies, accounting for the strongest correlations between absorption and emission; (ii) overdense gas filaments connecting galaxies, driving the excess of LAEs at a few times the virial radius and the modulation of the luminosity and cross-correlation functions for strong absorbers; (iii) an enriched and more diffuse medium, accounting for weaker C IV absorbers farther from galaxies.