Strongest negative inductive effect group between trimethylammonium, ammonium and dimethylsulfonium groups
The inductive effect can be quantitatively measured by the Hammett equation

$$\sigma(\ce{X}) = \mathrm{p}K_\mathrm{a}(\ce{H}) - \mathrm{p}K_\mathrm{a}(\ce{X})$$

where $\mathrm{p}K_\mathrm{a}(\ce{X})$ refers to the $\mathrm{p}K_\mathrm{a}$ of $\ce{X}$-substituted benzoic acid and $\mathrm{p}K_\mathrm{a}(\ce{H})$ to the $\mathrm{p}K_\mathrm{a}$ of unsubstituted benzoic acid. A more electron-withdrawing group will lead to a more acidic carboxylic acid group, a lower $\mathrm{p}K_\mathrm{a}(\ce{X})$, and hence a more positive $\sigma$ coefficient.

Values for a wide range of substituents in the meta and para positions have been tabulated in Table I of Ref. 1. Also included are Swain and Lupton's $F$ ($F$ for field) parameters which are designed to remove the influence of resonance effects on the original Hammett coefficients $\sigma$ (given in the same table; see Ref. 2 for original discussion).

$$\begin{array}{ccccc} \hline
\text{Entry number} &amp; \text{Substituent} &amp; \sigma_\mathrm{m} &amp; \sigma_\mathrm{p} &amp; F \\ \hline
\text{main text, p 167} &amp; \ce{NMe3+} &amp; 0.88 &amp; 0.82 &amp; 0.89 \\
58 &amp; \ce{NH3+} &amp; 0.86 &amp; 0.60 &amp; 0.92 \\
241 &amp; \ce{SMe2+} &amp; 1.00 &amp; 0.90 &amp; 0.98 \\
15 &amp; \ce{F} &amp; 0.34 &amp; 0.06 &amp; 0.45 \\ \hline
\end{array}$$

So, perhaps the answer should be $\ce{SMe2+}$. I don't have a good explanation for why, given that sulfur is less electronegative than nitrogen. I also do not think that the difference between $\ce{NMe3+}$ and $\ce{NH3+}$ can solely be attributed to the inductive effect of the methyl groups, as it is quite possible that there are solvation or hydrogen bonding effects that affect the $\mathrm{p}K_\mathrm{a}$ values. The bottom line is that I don't think this can be rationalised as simply as the question seems to want.

References


Hansch, C.; Leo, A.; Taft, R. W. A survey of Hammett substituent constants and resonance and field parameters. Chem. Rev. 1991, 91 (2), 165–195. DOI: 10.1021/cr00002a004. (there is a non-paywall copy here)
Gardner Swain, C.; Lupton, E. C. Field and resonance components of substituent effects. J. Am. Chem. Soc. 1968, 90 (16), 4328–4337. DOI: 10.1021/ja01018a024.