We study the source-subtracted near-infrared and X-ray background fluctuations of the COSMOS field using data from the Spitzer SPLASH program ($sim$1272 hours) and Chandra COSMOS Legacy Survey (4.6 Ms). The new auto power spectra of the cosmic infrared and X-ray background fluctuations reach maximum angular scales of $sim$ 3000$$ and $sim$ 5000$$, respectively. We measure the cross power spectra between each infrared and X-ray band and calculate the mean power above 20$$. We find that the soft X-ray band is correlated with 3.6 and 4.5$mu$m at $sim$ 4 $sigma$ significance level. The significance between hard X-ray and the 3.6$mu$m (4.5$mu$m) band is $sim$2.2 $sigma$ ($sim$3.8$sigma$). The combined infrared (3.6 + 4.5$mu$m) data are correlated with the X-ray data in soft ([0.5-2] keV), hard ([2-7] keV) and broad ([0.5-7] keV) bands at $sim$5.6$sigma$, $sim$4.4$sigma$ and $sim$6.6$sigma$ level, respectively. We compare the new measurements with existing models for the contributions from known populations at $z$$<$7, which are not subtracted. The model predictions are consistent with the measurements but we cannot rule out contributions from other components, such as Direct Collapse Black Holes (DCBH). However, the stacked cross-power spectra, combining other available data, show excess fluctuations about an order of magnitude on average at $sim$4$sigma$ confidence at scales within $sim$300$$. By studying the X-ray SED of the cross-power signal, assuming no significant variation from the infrared, we find that its shape is consistent with DCBHs.
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