Ion exchange chromatography is the best method to detect HbA1c.
Ion-exchange chromatography allows the separation of ionizable molecules according to differences in charge. It involves the use of a column which contains a matrix consisting of resin-bound charged groups.
If the charged group is anionic or negatively charged, it is called a cation exchanger and is used in cation exchange chromatography where proteins with a net positive charge migrate through the matrix more slowly than those with a net negative charge due to retardation of the migration of the former which is attracted to the negative charges bound to the resin.
Cation exchange chromatography is used for negatively charged HbA1c estimation and is used as a diagnostic tool for diabetes mellitus.
Glycated hemoglobin, reported as HbA1c, has been used to monitor glycemic control in patients with diabetes for many years. HbA1c results from the attachment of glucose to the N-terminal valine of the hemoglobin β-chain.
The concentration of HbA1c depends on both the concentration of glucose in the blood and the lifespan of the erythrocyte. Since the half-life of an RBC is 60 days, the level of glycated hemoglobin reflects the mean blood glucose concentration over the preceding 6 to 8 weeks.
Normal glucose tolerance is characterized by an HbA1c < 5.7%; any value of HbA1c equal to or exceeding 6.5 % is diagnostic of the patient being diabetic.
Also, ion exchange chromatography has the advantage of separating hemoglobin variants into peaks with the least interference by other hemoglobin variants; its disadvantage is that it is temperature dependent.

Other options:

Electrophoresis is an electrochemical process where macromolecules or colloidal particles depending on the electric charge migrate in a solution under the influence of an electric current. It can also be used for HbA1c estimation, its advantage being able to identify different variants of hemoglobin and disadvantage being interference of the process by fetal hemoglobin(HbF).
Immunoassays are used to quantify molecules based on the specificity and selectivity of antibody reagents generated. It can provide quantitative estimates of HbA1c but HbF produces falsely low results and hemoglobin variants such as HbS and HbC may cause a false increase in HbA1c measurements.
Affinity chromatography is a type of liquid chromatography. It involves the passing of a matrix through a solution that consists of the molecules of interest. These molecules would have a specific affinity for ligands present in the matrix and bind with them and end up getting separated from the solution. It can be used to measure HbA1c without being affected by temperature. High levels of HbF seen in thalassemia may interfere with its result.

Reference: Lehninger Principles of Biochemistry, 7th Edition (Page 396, 397)

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