Where can I find information about parish constables?

First read Ann E. Whetstone, Scottish County Government in the Eighteenth and Nineteenth Centuries (John Donald, 1981), which has chapters on the Justices of the Peace and Commissioners of Supply – the two bodies which administered the parish constable system in Scotland. If you wish to look in details at the work of parish constables in a particular county, you should look at Justice of the Peace records and Commissioners of Supply records for that county. Depending on the county these may be with a local authority archive or the National Records of Scotland (NRS). You might also consult J. A. Haythornthwaite Scotland in the Nineteenth Century: An Analytical bibliography of material relating to Scotland in Parliamentary Papers 1800-1900 (Scolar Press, 1993) for material in parliamentary commissions.