For budget, don't go with a laptop unless portability is essential for you. Although the performance gap between laptops and desktops has shrunk with recent CPU and especially GPU series, a laptop capable of good video editing will still cost a lot.
I'm assuming that you're looking for something under ₹70,000 (1029 USD).
For price, I'd highly recommend building your own desktop. You'll probably save a few hundred US dollar in labor right there—not so relevant for multi-thousand dollar machines, maybe, but for a budget device it's OK.
The recommended requirements for After Effects are modest, simply a multicore CPU and 16 GB RAM. To get good performance, you'll probably need a little more than that. I'd recommend an i7 CPU (or the AMD equivalent).
If you step back a generation, you should be able to grab one of the best Intel CPUs of its generation, the i7-7700k, for about $250 used or even new. For example, here.
For RAM, I'd go with 16 GB of DDR4, which should be around $150.
For your GPU, try getting a used 1060 for about $200. Depending on what you're doing in After Effects, a GPU could be essential or barely necessary, but CPU is usually a lot more important, so this is a compromise.
For the motherboard, you might as well get an H370. Motherboards are cheap to begin with, and anything lower will set future upgrades back unnecessarily. For example, here for $132.
For hard drives, I'd get one fast working SSD and one large HDD for storage. You can get a 2 TB HDD (7200 RPM) for about $50, and a 500 GB SSD for only $150 or so.
You can probably grab a budget case for about $70.
This totals about $1050 for a mostly new system. It should be very much capable of dealing with After Effects. It's slightly over your maximum (and I haven't included fans, power supply, etc.) but you can slice a little off by getting a lower tier motherboard (save $70), or a 250 GB SSD (save $70), or by getting the RAM used. Using a 6700k (two generations older, but similar speeds and can be overclocked anyway) could also save you a little.
I won't talk about fans, etc., since they'll contribute relatively little to the price.
If you really need a mobile system, it's going to be much harder to find a good one. There are a few good options, though, such as the Acer Aspire VX 15. This has a 1050 Ti GPU, about 16 GB of RAM, and a 7th-generation i7 CPU. Storage is minimal, though, so you'll end up needed an external hard drive, and as a laptop its performance will certainly be lower than than a desktop of similar price.