Optical depth variations in the Galactic neutral interstellar medium (ISM) with spatial scales from hundreds to thousands of astronomical units have been observed through HI absorption against pulsars and continuum sources, while extremely small structures with spatial scales of tens of astronomical units remain largely unexplored. The nature and formation of such tiny-scale atomic structures (TSAS) need to be better understood. We report a tentative detection of TSAS with a signal-to-noise ratio of 3.2 toward PSR B1557$-$50 in the second epoch of two Parkes sessions just 0.36 yr apart, which are the closest-spaced spectral observations toward this pulsar. One absorption component showing marginal variations has been identified. Based on the pulsars proper motion of 14 mas $rm yr^{-1}$ and the components kinematic distance of 3.3 kpc, the corresponding characteristic spatial scale is 17 au, which is among the smallest sizes of known TSAS. Assuming a similar line-of-sight (LOS) depth, the tentative TSAS cloud detected here is overdense and overpressured relative to the cold neutral medium (CNM), and can radiatively cool fast enough to be in thermal equilibrium with the ambient environment. We find that turbulence is not sufficient to confine the overpressured TSAS. We explore the LOS elongation that would be required for the tentative TSAS to be at the canonical CNM pressure, and find that it is $sim5000$ -- much larger than filaments observed in the ISM. We see some evidence of line width and temperature variations in the CNM components observed at the two epochs, as predicted by models of TSAS-like cloud formation colliding warm neutral medium flows.
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