Active cathodal HD-tDCS over left DLPFC cortex will be delivered for 10 days (3 sessions per week). The 4 × 1 montage using small circular electrodes (diameter 1 cm) will be applied with the cathode placed centrally over F3. The current intensity will be set at 0.5 mA for a total of 20 minutes (30 s ramp up/down).

Sham HD-tDCS will be delivered over pre-SMA or left-dlPFC cortex for 10 days (3 sessions per week). The same electrodes placement as well as the stimulation set-up will be used as in the active stimulation conditions, but the current will be applied for 30 s and will be ramped down (0 mA) during the rest of the session without the participants awareness. Each Sham session will last 20 minutes.

The Stop Signal Task is a computerized task evaluating inhibitory control. The task is structured in line with the consensus guide of SST (Verbruggen et al., 2019) and it will be performed on PsychoPy® software (Open Science Tools Ltd., Nottingham, UK). The task duration will be approximately 14 minutes. The Stop Signal Task will yield the following measures: stop signal reaction time, calculated in milliseconds by subtracting a mean Stop Signal Delays from the observed mean reaction times in no-stop trials; go accuracy; go reaction times; Stop Signal Delay.

The Short Sensory Profile 2 (Dunn, 2014) is a parent report questionnaire for evaluating the sensory processing pattern in children aged 3-14 years. It contains 34 items. Scores are assigned on a five-point Likert scale and range from "always = 0" to "often = 1" to "sometimes = 2" to "rarely = 3" to "never = 4". Low scores are indicative of frequent dysfunctional behavior. Based on a bell curve normed distribution, the raw score total for each quadrant can be classified as "much less than others" (lower 2%), "less than others" (between 1 SD and 2 SD below the mean, accounting for 14% of the normative sample), "just like the majority of others" (± 1 SD from the mean and accounting for 68% of the normative sample), "more than others" (between 1 SD and 2 SD above the mean), and "much more than others" (upper 2%).

The Behavior Rating Inventory of Executive Function (Gioia et al., 2015) is a parent report questionnaire consisting of 63 items for an ecological and comprehensive evaluation of executive functions in children aged 5-18 years. The tool encompasses 63 items evaluating inhibition, self-monitoring, shift, initiation, working memory, emotional control, planning, task-monitoring, and organization of materials. Items are further dived into 4 indices as follows: the Behavior Regulation Index, the Emotion Regulation Index, the Cognitive Regulation Index, and the Global Executive Composite. Raw scores of each scale and index are converted into T scores (M = 50, SD = 10) and percentiles. For all clinical scales and indices, T scores from 60 to 64 and from 65 to 69 are considered respectively mildly elevated and potentially clinically elevated while T scores at or above 70 are clinically significant.

The Sleep Disturbance Scale for Children (Bruni et al., 1996) is a parent report questionnaire for evaluating the sleep functioning of children and adolescents aged 6-16 years. The tool investigates the occurrence of sleep disturbances in the previous six months throughout 26 items on a five-point Likert scale (1 = least severe and 5 = most severe). It encompasses the following scales: difficulty in initiating and maintaining sleep, sleep-disordered breathing, disorders of arousal, sleep-wake disorders, disorders of excessive somnolence, and sleep hyperhidrosis. The sum of all items provides a total raw score ranging from 26 to 130, with higher scores indicating more sleep difficulties. A T score of >70 is clinically significant while T scores under 60 or ranged 61-69 are respectively in the average or borderline range.

The Child Behaviour Checklist/ 6-18 (Achenbach and Rescorla, 2001) is a parent report questionnaire to evaluate behavioral and psychopathological symptoms during the preceding 6 months in individuals aged 6-18 years. It includes 113 items on a three-point Likert scale (0 = not true; 1 = somewhat or sometimes true; 2 = very true or often true). According to the cut-off thresholds of Achenbach and Rescorla (2001), T-scores > 69 were classified as clinically relevant, t-scores between 65 and 69 were classified as borderline, and T-scores < 65 indicated non-clinical symptoms. For the internalizing problems, externalizing problems, and total problems scales, T-scores > 63 were classified as clinically relevant, T-scores between 60 and 63 were classified as borderline, and T-scores < 60 indicated non-clinical symptoms.

The Childhood Autism Rating Scale-2 (Schopler et al., 2010) is a rating scale for symptoms related to ASD. Higher scores indicate more severe symptoms of ASD. The instrument is designed for children aged 2-6 years or in individuals with ASD and low functioning (IQ ≤ 79 and regardless the child's age - Standard Form), and individuals with ASD and high functioning (IQ>80 - High Functioning Form). Both versions contain 15 items rated on a 4-point scale with higher scores revealing more severe symptoms related to ASD. The total raw score is converted into standard score within three ASD severity levels: no or minimum symptoms of ASD (15-29.5 or 15-27.5 with >13 years for the standard form; 15-27.5 for the high functioning form) mild to moderate symptoms of ASD (30-30.6 or 28-34.5 with >13 years for the standard form; 28-33.5 for the high functioning form), and moderate to severe symptoms of ASD (>35 or >37 with >13 years for the standard form; >34 for the high functioning form).

The Parenting Stress Index Short Form (Abidin, 1997) is a self-report questionnaire designed to evaluate parental stress levels in parents of children aged 1 month to 12 years. The instrument is used in both clinical and research settings. It contains 36 items rated on a five-point Likert scale (1 = strongly disagree and 5 = strongly agree). Items encompass three subscales as follows, parental distress or the experienced distress in the role of being a parent, difficult child linked to the child's behavioral problems, and parent-child dysfunctional interaction. The sum of all items results in the Total Stress score. The total raw score is converted into percentile score; percentile ≥85 is considered as clinically significant.

Resting-state EEGs will be recorded in a sound-attenuated, electrically shielded room to minimize external noise and interference.