The goal of this clinical trial is to to obtain a significant decrease in seizure frequency in patients with refractory focal epilepsy after applying treatment of cathodal tDCS, compared to sham stimulation drug-resistant epileptic patient. The main questions it aims to answer are:

• Changes in quality of life
• Percent of newly reported side effects after the stimulation period
• Scores in epilepsy severity. Participants will be randomized in a cross-over, and will receive 10 days of tDCS or Sham. Each day will allow 2 periods of 20 minutes stimulation separated by 20 minutes off (with 40 minutes of cathodal stimulation total).

Inclusion Criteria:

1. Patient, parents or legal representative who have given written informed consent;
2. Age: ≥ 9 years;
3. Patients with drug-resistant focal epilepsy with no evolutive brain lesion and no surgical indication or with a previous surgical failure, refusing surgery or with a planned surgery compatible with the total duration of this study;
4. SEEG previously performed before inclusion with an adequate definition of the epileptogenic zone with all data required (pre-SEEG MRI, CT-scan or MRI with electrodes during SEEG and SEEG files) for personalization ;
5. Patient having a pre-SEEG 3D-T1 MRI and CT-scan with electrodes during SEEG available; This MRI can be done specifically for this trial or might be reused from EPINOV or NEURO7T trial)
6. For patients with VNS, experiencing no response or partial response, and for whom the stimulation parameters have been stable for at least 6 months
7. A research MRI scan that is suitable for navigated brain stimulation (NBS) and generation of electrical fields including dMRI for tractography;
8. Number of seizures ≥3/month during the baseline (before the first session of tDCS treatment);
9. Patient having stable medications for epilepsy 4 weeks before the baseline (except rescue treatment);
10. Patient's IQ, which in the investigator's opinion will enable questionnaires and neuropsychological assessments to be carried out;
11. Patient able to understand, speak and write in French;
12. Patient able to follow study's procedure;
13. Patient beneficiary or affiliated to a health insurance plan.

Exclusion Criteria:

1. Patients with seizures of generalized onset in the last 12 months;
2. Patient with multifocal epileptogenic zones, bilateral epileptogenic zone, or poorly defined epileptogenic zone. The epileptogenic network should not be restricted to the orbito frontal cortex or cingulate cortex;
3. Patients with psychogenic nonepileptic seizures;
4. Patient presenting a contraindication to MRI 3T (patient having a pacemaker, metallic foreign bodies, non-removably implanted electronic medical devices, claustrophobia, inability to remain in supine position, vagus nerve stimulator even when switched off is a contraindication for MRI 3T. EPINOV or NEURO 7T trial patients, who have accepted for their data to be reused, can be included even while wearing a VNS device) ;
5. Substance use abuse that may include alcohol , opioids (heroin, fentanyl) stimulants (Cocaine, methamphetamine) , hallucinogens (LSD, psilocybin (magic mushrooms), MDMA (Ecstasy))
6. Patient presenting a serious intercurrent pathology and/or a progressive brain tumor
7. Patient having damaged skin or scalp that may interfere with tDCS stimulation (e.g., eczema, lesion);
8. Patient having any cranial metal implants such as shrapnel or surgical clips (excluding <1 mm thick epicranial titanium skull plates and dental fillings) or medical devices (i.e. cardiac pacemaker, deep brain stimulator, medication infusion pump, cochlear implant)
9. Patient having previous surgeries opening the skull leaving skull defects capable of allowing the insertion of a cylinder with a radius greater or equal to 5 mm;
10. Any condition that makes the study subject, in the opinion of the investigator, unsuitable for the study including presence of any disease, abnormality, medical or physical condition that, in the opinion of the investigator, may adversely impact, compromise, interfere, limit, affect or reduce the safety of the subject, the integrity of the data ;
11. Person protected by articles L1121-5, L1121-6 of Public Health Code (pregnant or breastfeeding woman, deprived of liberty by judicial decision, situations of social fragility, adults unable or unable to express their consent, person under judicial safeguard (article L1122-2)).