  In order to probe the activity of the inner disk flow and its effect on the
neutron star surface emissions, we carried out the timing analysis of the Rossi
X-Ray Timing Explorer (RXTE) observations of the millisecond X-ray pulsar XTE
J1807--294, focusing on its correlated behaviors in X-ray intensities, hardness
ratios, pulse profiles and power density spectra. The source was observed to
have a serial of broad "puny" flares on a timescale of hours to days on the top
of a decaying outburst in March 2003. In the flares, the spectra are softened
and the pulse profiles become more sinusoidal. The frequency of kilohertz
quasi-periodic oscillation (kHz QPO) is found to be positively related to the
X-ray count rate in the flares. These features observed in the flares could be
due to the accreting flow inhomogeneities. It is noticed that the fractional
pulse amplitude increases with the flare intensities in a range of $\sim
2%-14%$, comparable to those observed in the thermonuclear bursts of the
millisecond X-ray pulsar XTE J1814--338, whereas it remains at about 6.5% in
the normal state. Such a significant variation of the pulse profile in the
"puny" flares may reflect the changes of physical parameters in the inner disk
accretion region. Furthermore, we noticed an overall positive correlation
between the kHz QPO frequency and the fractional pulse amplitude, which could
be the first evidence representing that the neutron-star surface emission
properties are very sensitive to the disk flow inhomogeneities. This effect
should be cautiously considered in the burst oscillation studies.
