  We present the synthesis and a detailed investigation of structural and
magnetic properties of polycrystalline Ba(TiO)Cu$_{4}$(PO$_{4}$)$_{4}$ (BTCPO)
via x-ray diffraction, magnetic susceptibility, heat capacity, and $^{31}$P
Nuclear Magnetic Resonance (NMR) measurements. BTCPO has a 2D layered structure
with interlinked Cu$_{4}$O$_{12}$ tetramer units. A broad maximum is observed
around 16.5 K in our magnetization data accompanied by a sharp anomaly around
$T$ = 9.5 K in the heat capacity. An anomaly at $T$ = 9.5 K is also found in
the temperature dependence of the $^{31}$P NMR spin-lattice relaxation rate
$1/T_1$. A power law behavior for the heat capacity as well as for the $^{31}$P
$1/T_1$ below the ordering temperature could be obtained. The $^{31}$P NMR
lineshape is asymmetric and the NMR shift tracks the bulk spin-susceptibility.
We estimated the isotropic and axial components of the hyperfine coupling
tensor to be as the $A^{iso}_{hf} \backsimeq 6794$ $\rm{Oe/\mu_{B}}$ and
$A^{ax}_{hf} \backsimeq 818$ $\rm{Oe/\mu_{B}}$, respectively.
