Competitive charge density waves in the doped kagome superconductor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>CsV</mml:mi><mml:mrow><mml:mn>3</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub

Unconventional charge density waves (CDWs) have been observed in the kagome superconductor ${A\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ $(A=\mathrm{K}, \mathrm{Rb}, \text{or} \mathrm{Cs})$, which exhibit extraordinary symmetry breaking and intertwine with superconductivity (SC). Here, via $^{51}\mathrm{V}$ nuclear magnetic resonance (NMR), we reveal that a new CDW modulation is developed locally around dopants in ${\mathrm{CsV}}_{3\ensuremath{-}x}{\mathrm{Ti}}_{x}{\mathrm{Sb}}_{5}$, which leads to the suppression of the long-range triple-Q CDW. With slight Ti substitution $(x&lt;0.09)$, a rapid increase in Knight shift and a progressive decrease in $1/{T}_{1}T$ are observed, which is beyond the simple picture of the suppression of the triple-Q CDW. Above $x=0.12$, while the CDW transition is absent in specific heat measurements, a gap behavior is still observed in the local spin susceptibilities. By quantitatively analyzing the doping-dependent NMR line shape and $1/{T}_{1}T$, we propose that a competitive CDW with unidirectional modulation is locally formed around Ti dopants, which is key to explaining the unusual evolution of the CDW and SC in ${\mathrm{CsV}}_{3\ensuremath{-}x}{\mathrm{Ti}}_{x}{\mathrm{Sb}}_{5}$. In this picture, the persisting gap behavior above $x=0.12$ comes from the short-range CDW matrix. In addition, our present NMR results highlight the role of the next-nearest-neighboring V-V interaction in CDW driving. All these findings substantiate vanadium-based kagome superconductors as strongly coupled electron-lattice systems, which is a basis for understanding unconventional CDWs and their role in SCs.