The Northern Ireland-based handler will face a BHA disciplinary panel hearing on September 19 after the nine-year-old, who is owned by Michael McConville, was found to have cobalt, a prohibited substance, above the permitted threshold in a urine sample before it was due to run in the Foxhunter Chase.
Speaking in a statement, the trainer said: "Both myself and my son, Michael, have been notified by the British Horseracing Authority that a hearing will take place on September 19 regarding the incident at the Cheltenham Festival and our horse, Anseanachai Cliste, which prevented him contesting the Foxhunter Chase.
"We have to date co-operated with the BHA and their team detailing with the issue and will continue to do so.
"We look forward to the conclusion of this unfortunate occurrence and will fully assist the disciplinary panel of the British Horseracing Authority with their hearing, answer any outstanding questions and accept their decision on the matter."
The horse was withdrawn from the race by order of the stewards, with a BHA report stating they "could not be satisfied that the horse had been administered only normal feed and water on race day".
Both face charges over allowing or causing the administration, or conniving in the administration of prohibited substances, having such items in their possession on a racecourse, on a race day and attempting to obstruct the proper administration or control of racing specifically by deliberately misleading, or endeavouring to mislead stewards and/or a BHA employee.
Michael McConville will also have to answer whether he failed to act in the interests of the horse's best health and welfare by administering substances, namely Adrenal Cortex, without veterinary consultation or advice.
For his part, Stephen McConville has to answer if he was complicit in assisting, aiding and/or engaging the responsible person (his son) for the horse in violations of the equine anti-doping rules.
Anseanachai Cliste had won eight successive point-to-points prior to his arrival at Prestbury Park in March and went on to win the Ulster National at Downpatrick nine days later.