Does the position of a functional group in an organic compound have any effect on the compound's heat of combustion?
The exhaustive combustion of an organic compound consisting of carbon and hydrogen only will yield carbon dioxide and water.  Thus, if the heat of formation for isomers differ from each other, then the heat of combustion will differ, too.
This entry in the English Wikipedia states, for example
$\pu{−146.9 kJ mol^{-1}}$ for n-pentane, $\pu{−154.4 kJ mol^{-1}}$ about isopentane (methylbutane), and $\pu{−167.8 kJ mol^{-1}}$ for neopentane / dimethylpropane; all of same number of atoms $\ce{C5H12}$ (pentane), but with different connection of methyl groups to a backbone in common.  The very table continues for other branched isomers of alkanes, too.

Possibly there is a misunderstanding between the computation of heat of formations from paper (or, in a computer program), on one hand, and the experimental determination of these properties, too.
For the former, the approach typically taught in schools to determine the enthalpy of formation is

to imagine the reaction of $\ce{C_xH_y}$ with $\ce{O2}$ to yield $\ce{CO2}$ and $\ce{H2O}$
to look up the standard heat of formation of $\ce{CO2}$ and $\ce{H2O}$, hopefully with a discern between water as gas and water as liquid
to apply Hess's law to compute $\Delta_fH^\circ$ for $\ce{C_xH_y}$ with the convention that $\Delta_fH^\circ$ for elements in their most stable form (here, oxygen) is set zero

This approach however is an approximation which does not account how the atoms are connected with each other and their neighbours, or bond order; as if e.g., a carbon in acetylene does not differ from the carbon in methane.
If one leaves the imaginary reaction to $\ce{CO2}$ and $\ce{H2O}$, there are empirical increment systems based on experimentation, set to improve this approximation when computing this on paper.$^*$  With the advent of quantum chemistry, it is up to you to select a theory suitable enough to compute this in silico, too (example by MOPAC).
Among the classic approaches to determine experimentally the heat of formation via the heat of reaction (again, Hess' law is applied) is bomb calorimetry.  Here, exhaustive combustion a known quantity of your compound takes place in an atmosphere of pure high-pressure oxygen.  It is one of the experiments students may encounter early when studying physical chemistry.
$^*$  Publications like 1993ChemRev2419, 2011JPhysChemA10576, or 2012JPhysChemA7196 review / present extensions, or are basis for more recent work, too (cited by below the landing page of the publication) in addition to the increment system above mentioned Wikipedia entry currently presents.  Of course, one equally may  adjust existing / establish a new increment systems, e.g., as combination of own work (bomb calorimetry) and using data already recorded by others and presented in primary references (articles) and tables (e.g., CRC Handbook of Chemistry and Physics, NIST Webbook Chemistry)